The club are looking to recoup fines from UEFA that are set to total 17,000 euros (£13,000) from the supporters who ran onto the pitch during matches.
Newcastle were first fined 7,000 euros after 21-year-old named Steven Arkle ran naked on to the pitch during a match against Greek side Atromitos on 30 August.
They are now expected to be fined a further 10,000 euros after a 35-year-old called John Parkinson entering the playing area wearing only an England shirt during their October clash with Bordeaux.
Both men have pleaded guilty to public order offences and will be sentenced in December.
Neither man is a season ticket holder or a member of the club.
"We will be actively seeking compensation through the court for the financial penalty imposed by UEFA," confirmed Newcastle's head of security Steve Storey.
"People who think that selfishly running on the pitch is fun or funny should realise it is not. It's a criminal offence which disrupts the game.
"It offends thousands of people inside the stadium, particularly when they run on naked. It's beamed live throughout Europe and it has brought embarrassment to the club given it's the first time we've been back in Europe for many years.
"We are taking legal advice to consider taking civil action against both men.
"The club are really disappointed that these two, who are not season ticket holders or members of the club, decided to carry out these acts."
Top 10 sporting interruptions
Protester interrupts University Boat Race, 2012
Trenton Oldfield swam into the middle of the 158th University Boat Race, causing it to be stopped. Oldfield, lucky to avoid being struck by the rowers, was hauled out of the water and arrested, while Cambridge eventually won a race which had long since been tainted. Just last week Oldfield was sentenced to six months in prison.
Priest interrupts Grand Prix, Olympic Marathon, 2003-4
Neil Horan's attempts to spread the word of Christianity put his life at risk in 2003 when he ran across the track during the 2003 British Grand Prix. The incident shocked the sport, but just a year later Horan reappeared, running into the middle of the 2004 Olympic marathon in Athens and pushing then-leader Vanderlei de Lima into the crowd, costing him his chance of winning a gold medal.
Streaker Erica Roe interrupts Twickenham Test, 1982
Few streakers are so well-remembered that they merit their own Wikipedia page, but Roe does. She attributed her 1982 dash across the Twickenham turf to alcohol, and the Observer reported last year that she now lives in Portugal with her family farming organic sweet potatoes.
Bomb scare interrupts 1997 Grand National
Not long before the 150th running of the Grand National was scheduled, organisers received two warnings about a bomb scare within the racecourse area. There was no option but to call off the event and evacuate the 60,000 people in attendance, but the race was re-staged two days later with Lord Gyllene taking a commanding victory.
Cat interrupts Premier League match, 2012
Liverpool's Premier League match against Tottenham was brought to an unusual halt by the arrival of a cat on the field of play at Anfield. The grey and white moggy sauntered on to the pitch 11 minutes into the contest and ran around happily for a minute, and became a phenomenon on Twitter with several thousand followers of a spoof account.
Earthquake interrupts 1989 World Series
Baseball's showpiece had reached game three, and a capacity crowd had taken their place in Candlestick Park in San Francisco for the showdown between the San Francisco Giants and the Oakland Athletics. But shortly before the game was to begin an earthquake struck. The natural disaster went on to claim 42 lives across the west coast of America, as well as causing panic in the stadium. The game was eventually restaged 10 days later, with Oakland winning in part of a 4-0 march to the crown.
Bees interrupt Sri Lanka v England Test, 2007
England were battling against Kumar Sangakkara and colleagues on day four of the opening Test in Kandy when a swarm of bees buzzed into the Asgiriya Stadium, causing alarm. The players and umpires to a man dropped flat on the floor, waiting anxiously for the swarm to pass. When they did and play resumed, England went on to lose a keenly-fought Test.
The Fan Man interrupts Bowe and Holyfield's title bout, 1993
Riddick Bowe and Evander Holyfield met on a November night in Las Vegas in a heavyweight showdown, but after six rounds of action the seventh was interrupted when James Jarrett Miller dropped by parachute into the arena at Caesar's palace and into the ring. Security entourages leapt in and knocked Miller unconscious. The fight eventually continued and Holyfield handed Bowe the first defeat of his career by a decision after 12 rounds.
Cyclists interrupt the Tour de France, 1998
The 1998 Tour de France had been billed the Tour du Dopage after a series of doping scandals culminating in the expulsion of the Festina team. With the race descending into farce and the riders aggrieved by the treatment of the TVM team following a police raid on their hotel, the cyclists staged their own protest. Riders began stage 17 at a snail's pace, before grinding to a complete halt after 20 miles of 'racing'. The race eventually resumed, with Marco Pantani of Italy winning the yellow jersey for that year.
Streaker interrupts cricket match in Australia, 2008
A one-day international in Brisbane between Australia and India was interrupted in 2008 when a streaker surged on to the pitch and towards the players. Not his finest move. With Andrew Symonds at the crease for the home side, Robert Ogilivie was dealt an unwelcome surprise when the batsman shoulder-charged the streaker and sent him crashing to the ground.
Ogilivie was fined the equivalent of £700 for his indiscretion - Symonds escaped any punishment, with a Cricket Australia spokesman explaining; "Symonds was dealing with self-preservation, which we support 100 per cent."