The 23-year-old is set to move to Old Trafford in a deal worth €21 million ($27m) plus add-ons.
The Belgium youth international is travelling to Manchester and will sign a five-year contract after undergoing a medical.
Sources have told ESPN that Lammens' arrival does not necessarily mean that one of André Onana or Altay Bayindir will leave before the transfer deadline.
United also have 39-year-old Tom Heaton as part of their senior goalkeeper group.
Sources have told ESPN that Galatasaray have been exploring a deal for Onana over the weekend after missing out on signing Manchester City goalkeeper Éderson.
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The Brazil international is set to leave the Etihad Stadium to join Fenerbahce.
Galatasaray have also shown interest in Diogo Costa and Yann Sommer and remain keen to sign a goalkeeper to bolster their squad ahead of their return to the Champions League.
A source close to Onana told ESPN on Sunday that the Cameroon international does not anticipate leaving before the end of the window and wants stay at Old Trafford to fight for his place.
However, United will listen to any reasonable offers for the 29-year-old and Galatasaray could yet make a late bid.
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