United are set to sign Bayindir from Fenerbahce for around €4.9m ($5.29) while Henderson is on the brink of joining Palace in a permanent deal worth £20m.
Bayindir has already completed his medical and is ready to sign once Henderson's move is complete.
Henderson was named on the bench for United's 3-2 win over Nottingham Forest on Saturday and travelled to London after the game to undergo a medical and negotiate personal terms. Palace sporting director Dougie Freedman was in the crowd at Old Trafford on Saturday.
Sources have also told ESPN that United are exploring the possibility of signing a left-back before Friday's transfer deadline to compensate for the loss of Luke Shaw.
Shaw could be out until November with a muscle injury while Tyrell Malacia is facing a similar spell on the sidelines because of a knee injury.
Third choice Brandon Williams, who was part of the squad during the preseason tour of the United States, has joined Ipswich Town on loan. It meant Diogo Dalot, usually a right-back, was forced to fill in on the left against Forest.