"After consultation between Avram Grant, club doctor Bryan English and physios Dave Hancock and Thierry Laurent, Cole resumed and took full part in the final training game, only disappearing down the tunnel after the players had listened to Avram's address and been stood-down for a final kickaround."
Wayne Bridge, fellow England left back, is available to replace Cole if he does not fully recover in time, but the defender is expected to be fit and play in his second Champions League final after being on Arsenal's losing side two years ago.
United go into the match with no injury concerns and start as favourites after beating Chelsea to the Premier League title earlier this month.
Nemanja Vidic, United centre back, sat out their final training session on Tuesday night at the Luzhniki Stadium but is fit to play.
Giggs record
Alex Ferguson, United manager, said he has known for several days what his starting line-up will be and the hardest part of the build-up will be telling some of his players that not only are they not in the starting line-up but they will not be on the substitutes bench either.
"I think Uefa should bring in an 11-man bench as there is at the World Cup," Ferguson said.
"Because it is very difficult to leave six or seven players out."
Paul Scholes, who was suspended for United's 1999 triumph in the final against Bayern Munich, will start the match, while Ryan Giggs, who played in the 1999 game, is likely to be on the bench.
If Giggs does take the field, he will overtake Bobby Charlton's all-time club record of 758 appearances.