Sir Alex Ferguson is unwilling to meet the £38m release clause in Gaitan's contract and is looking to use the duo as makeweights to try to persuade Benfica to lower their asking price.
Full-back Fabio would join the Portuguese outfit on a one-year loan deal to gain some valuable game time.
Ferguson told the Telegraph: "Fabio will go on loan next season to give him concentrated first-team experience. We have already talked to him and he understands the value of playing regularly at a higher level than we can give him at the moment."
Striker Macheda spent the latter part of the current campaign on loan at Queens Park Rangers but failed to impress, and returned to Old Trafford after picking up an ankle injury.
Gaitan, 24, can play as a left-winger or an attacking-midfielder and is represented by agent Jorge Mendes, who helped take Cristiano Ronaldo and Nani to Manchester United.