Baines (28) has emerged as one of the finest left-backs in Europe this season and has two years left on his existing deal at Everton after this season. It is highly unlikely that David Moyes would sanction Baines' sale next month, but the player is expected to be the subject of some interest come the summer.
United refused to pay Everton's £15m valuation of Baines last summer, but he has subsequently had his best season yet.
Chelsea had hoped by now to announce that a deal to sell Daniel Sturridge to Liverpool had been agreed, but the move has again hit a snag over the sell-on fee. The deal is still expected to go through, but it has not been made straightforward by changing demands from the player's camp.
Manchester City duo Kolo and Yaya Toure join Newcastle's Cheick Tiote, Arsenal forward Gervinho and Wigan striker Arouna Kone in Lamouchi's selection ahead of the Elephants' pre-tournament trip to Abu Dhabi and subsequent friendly match with Egypt on January 14.
Abdul Razak (20) of Manchester City is also included a line-up that boasts Shanghai Shenhua striker Didier Drogba, Galatasaray's Emmanuel Eboue and Trabzonspor midfielder Didier Zokora, all of whom had spells in England with Chelsea, Arsenal and Tottenham.