United boss Alex Ferguson is a huge admirer of the left-back, who is out of contract in the summer and stalling over signing a new one-year deal at Stamford Bridge.
The Daily Mail reports that Ferguson is shocked that a player of Cole's stature has been allowed to run down his current contract and the Scot would jump at the chance to bring in a replacement for Patrice Evra, whose future at Old Trafford remains in doubt.
Cole is best friends with Wayne Rooney and the end of the 31-year-old's feud with Rio Ferdinand has also helped clear the way for Ferguson to take him to United. It all makes sense now...
Also featuring on the back page of the Mail are quotes from David Moyes, who has cranked up the hostility ahead of Sunday's Merseyside derby by claiming players like Luis Suarez are turning fans away from English football.
It's a big call to make, but Moyes has always held strong views about players who go down too easily, and ahead of the match at Goodison, he said he is worried about Suarez and his penchant for diving.
The Scot referenced the sending off of Jack Rodwell in last season's fixture after Suarez reacted dramatically to a challenge and said he believes the culture of players cheating to gain an advantage will eventually mean football loses spectators.
In most other papers is news of Roberto Mancini hitting back at his own players, after yesterday's reports of a mutiny at Manchester City.
The Sun's headline is 'Get it... or get out' while the Mirror goes for 'Like it or lump it', after Mancini made it clear to Micah Richards and his star players that they will be axed if they cannot adapt to his style of management.
Richards criticised the boss and his tactics in the wake of City's disappointing 3-1 defeat to Ajax in the Champions League during the week, but the Italian has been quick to respond and put his players back in their place.
“Maybe next time we play this system Micah can stay on the bench and we will use another player until Micah knows the system well," Bobby Manc said.
“If you are a top player it’s not important what system you use. If you don’t understand you’re not a top player and you can’t play for a top team.”
'John Terry - anti-racism campaigner' - a headline few could have dreamt of a week ago, but there it is today, on the pages of the Daily Mirror.
Terry, in the middle of serving a suspension for racially abusing Anton Ferdinand, will make a public show of support for the Kick It Out anti-racism campaign on Sunday.
Although he won't feature in the match against Manchester United, the Blues captain will use his programme notes to state his personal commitment to the cause, while extra statements in support of the campaign will also be contained in the programme.
After such a bad week for Chelsea, better news for the club comes in the Daily Telegraph, which reports that Pep Guardiola could be on his way to Stamford Bridge at the end of the season.
"Pep wants to manage in London and he is looking for the right project,” said a source familiar with Guardiola’s situation.
The former Barcelona boss has said he wants a season away from football but Chelsea are sure to be encouraged by these quotes and are set to revive their bid to lure him to Stamford Bridge for next season.
The paper also reports that Guardiola’s representatives have, through intermediaries, also made contact with Arsenal over the possibility of a future vacancy at the Emirates Stadium.
But Arsene Wenger's position at the Emirates Stadium is believed to be more secure than Roberto Di Matteo's across town, and Chelsea are favourites to land Guardiola.
A former Chelsea manager, Jose Mourinho, is set to step up his interest in Tottenham flyer Gareth Bale. Again.
Real Madrid have disappointed both domestically and in Europe so far this season and Mourinho is keen on making a big statement with the signing of Bale in a squad shake-up. The Mirror's figure on the Welshman's head is £50 million-plus.
Elsewhere, Aston Villa striker Darren Bent, who was stripped of the captaincy and then dropped by manager Paul Lambert, has revealed to The Sun that he will not ask for a transfer.
“Villa are a massive club and I always want to play for huge clubs," Bent said, cleverly keeping his options open on a move to at least eight other equally massive, or even more massive, Premier League clubs.
In other news, Arsenal are poised to end their 18-year association with Nike and sign a new £25m contract with rival kit suppliers adidas, according to the Daily Telegraph.
And finally, not everyone is as big a fan of Twitter as Joey Barton it would seem. Kyle Walker has turned his back on the social networking site after trolls got under his skin by claiming he is a lazy player.
The Tottenham defender said in the Daily Express that some posters on his account have no idea of the hours he puts in at the training ground.
“Some people were just having a bit too much to say in a way that showed they did not know how much work I was putting in.
“I am probably the first one in and the last one out every day. If that means doing gym or some extra swimming, I’m prepared to do that to make myself a better player.
“That is why I have come off Twitter. I thought I needed to concentrate on my own performance for a few weeks.
“When you have 250,000 people following you, not everybody is going to be happy, so you have to be thick-skinned.
“I want to concentrate on my football instead of tweeting and when it comes back right, I will probably go on there again.”