The Old Trafford side are battling for the signature of the defender with Arsenal, who have already submitted a similar offer for the Argentine international.
Ajax are reportedly holding out for a package of around £43m for the 24-year-old Argentina international. The Dutch champions have yet to officially respond to the most recent bids and continue to privately insist they do not want to sell the 24-year-old.
According to a report in GOAL, there is a feeling among those close to the player that the Dutch champions want to delay things for as long as possible in an attempt to spark even more of a bidding war between the Premier League rivals.
But United are confident the issues will be resolved, and the deal can be completed in the coming days.
Martinez is currently on holiday after a long season in which he won the Dutch League title under the current Manchester United boss. He is reportedly relaxed about the situation but expects that his club will allow him to move this summer.
The defender made it known that he wants to move to England and is expected to start pushing for a move if nothing changes soon.