The Scottish Premier League club accepted an offer for Russell from the Rams on Wednesday, but subsequent reports that the 23-year-old has put pen to paper are jumping the gun.
Russell, who has a year remaining on his contract at Tannadice, is currently away on holiday, but Press Association Sport understands that personal terms have been agreed and the player will undergo a medical at the Rams' Moor Farm training ground next week.
Russell's agent John Viola told Press Association Sport: "A fee has been agreed with Derby County and Johnny is going down there next week for a medical and to have a look around and look at the set-up.
"That's where we are at the moment, nothing has been signed.
"We are happy with what has been discussed so far and Johnny going down there sometime next week is the next step."
Russell has attracted interest from a host of clubs both north and south of the border, as well as from Italian side Catania, who finished eighth in Serie A last season.
Dundee United knocked back a couple of offers from Catania, while Derby's Championship rivals Huddersfield and Sheffield United also made unsuccessful moves for the player in August and January respectively.
When asked if it was possible that Russell might not end up at Pride Park, Viola added: "Of course, if another club showed an interest and met Dundee United's valuation of the player. Like I said, nothing has been signed.
"Johnny Russell is a very good player and he has attracted a lot of interest both from other clubs in England and abroad. It is well documented that a Serie A club has had bids turned down."