It was recently reported that the club were in advanced negotiations to sign Telles from Porto, but it appears that they have yet to finalise the transfer fee.
Porto are prepared to accept a reduced £23m fee for Telles, who has a £36.7m release clause on his contract, but United are reluctant to pay the sum outright.
The Red Devils have looked at the possibility of sending Diogo Dalot in the opposite direction as a makeweight, but Porto have declined the offer.
Hence, they are said to be looking at alternatives and Tagliafico has reportedly emerged as a potential target to strengthen the left-back department.
Luke Shaw and Brandon Williams have been the regular choices for Ole Gunnar Solskjaer, but the latter is a right-back by trade and has a weaker left foot.
Shaw, on the other hand, has impressed defensively in recent seasons, but he has not made much of an impact in the offensive scheme of things.
Elsewhere, he has also struggled with fitness concerns and that could be one of the prime reasons behind the pursuit of a new left-sided defender.
Tagliafico, who bagged five goals and seven assists last term, is available for a similar £23m fee to Telles, but Ajax may be willing to accept staggered payments.
At 1.72m, he does not have the height advantage, but he is still good in the air and won two aerial duels per league game on average last season.
Besides this, he managed more than two tackles per 90 minutes and he has the attributes to become a solid competitor to Shaw for the left-back role.
Stats from Transfermarkt.com and Whoscored.com