Milne, 28, has spent all of his career in Scotland, but Adkins is hopeful that he has persuaded the six foot two inch defender to join United.
He visited Glanford Park on Wednesday and United hope that the Falkirk defender will become their second summer signing penning a deal later on Friday.
Meanwhile, ex Manchester United youngster Michael Lea is on trial with United after being released by the Red Devils this summer. The 20 year old enjoyed a loan spell at Royal Antwerp last season and Adkins sees him as a replacement for Marcus Williams if the left back does not sign a new deal.
"He is here for a couple of days for us to have a close look at" confirmed manager Nigel Adkins.