The Leicester midfielder has been in inspired form this season, leading him to earn a call-up to the senior England squad.
United are just one of the clubs keen on signing the 22-year-old, and are thought to be in prime position to land his services.
The Athletic report that the positive relationship between United chief Ed Woodward and his opposite number at Leicester, Susan Whelan, could prove to be the catalyst to get the deal concluded in the next 12 months.
However all three of those clubs can offer Champions League football to the Foxes star – providing they qualify again next season – while United are currently some way behind all three and Leicester in the table.
That could prove decisive in any negotiations, while there are suggestions Maddison could yet extend his contract at the King Power, even if only for short-term financial gain.
Maddison fits the bill that United boss Ole Gunnar Solskjaer is looking for as a young, talented player hungry to succeed.
He has already had a hand in five goals for his club this season, scoring three times and providing two assists in his nine appearances in all competitions.
But a move to the Red Devils is likely to be dependant on the success of this season.
“Everybody is wondering what Manchester United are about and where they are going,” a prominent agent told The Athletic. “Each situation is different and for some players United is still the destination of choice. But more generally players are less willing to go there than in the past.
“Agents will be asking for more because they know that for the first time in a long time Man United need players more than players need them. They used to be in the stronger position but they now have a weaker hand and players can use that to their advantage in negotiations.”
Woodward recently admitted that United have to be wary of some players using the club for their own means in order to secure a better deal elsewhere.
When asked about the possibility by United We Stand , he said: “We’re usually after three players, so we might be talking to nine in reality.
“What you are referring to in the original question does happen, but it’s less likely to happen given our closed-door approach to recruitment targets.
“But it does exist and we have to be wary of that [players using the club].
“Sometimes, the amount of time a player or his agent invests into discussions, meetings and contracts shows that there is an interest.
“If it was only a flippant interest then they could go and put a fake story then go to a club president and go say ‘Look at who is in for me.’ That happens all the time as well.
“What sometimes also happens is that we do have a player in an agreed position, but his club refuse to sell and, because the club refuse to sell, the player then uses that to get a new contract.
“From our perspective, we have to try and see through it and make sure that the club is not being used.”