Aguero’s trophy-laden ten-year spell at the Etihad Stadium is edging to a close as the striker prepares to leave the Cityzens at the end of the season.
The Argentine will be available for free in the summer after not renewing his contract with City, which has put several clubs on red alert.
United are one of the teams looking to exploit the transfer market, with Ole Gunnar Solskjaer hopeful of assembling a squad able to compete for the Premier League title next season.
However, the Red Devils will have to overcome stiff competition from Chelsea, Paris Saint-Germain and Barcelona to bring Aguero to Old Trafford.
Despite enduring an injury-hit season, the 32-year-old is among the most lethal forwards in Europe’s top-five divisions and arguably one of the best marksmen to ever grace the Premier League.
Kun has netted 257 goals in 384 matches for City en route to becoming the club’s record goalscorer and is also the highest non-English scorer in the Premier League history.
He has yet to decide where he wants to continue his career, though, with plenty of options to choose between.
United could look to mirror the transfer deal for Edinson Cavani from the previous summer transfer window and add another household name to their star-studded attacking cast.
They reportedly see Aguero’s signing as payback for City taking Carlos Tevez away from Old Trafford 12 years ago.
It is understood that the player’s preference is to remain in the Premier League, which boosts United’s hope that they may pull off the impossible.