The former midfielder also believes that using Marouane Fellaini as a target man is not a long-term solution.
The Reds currently sit fourth in the table, seven points ahead of fifth-placed Liverpool but only two points behind rivals Manchester City who sit second.
They have impressed in the second-half of the season under manager Louis Van Gaal, although recent defeats to both Chelsea and Everton last time out have seen optimism curbed somewhat.
They do, however, look set to return to the Champions League at the first time of asking, although Savage says that is not good enough for them, merely a minimum requirement.
“I would say they will finish fourth this season,” he wrote.
“Yes, that's a significant improvement on last year, but I cannot believe fourth place, with Fellaini as the central piece of the jigsaw, is enough for a club of their stature. It should only be the bare minimum.”
As his comments suggest, the former midfielder also questions where the side are going if they continue to be so reliant on midfielder Marouane Fellaini.
The Belgian endured a poor start to his United career but has since become a key player under Van Gaal, helping to repay some of the £27.5 million (per the BBC) former manager David Moyes paid for him.
However, Savage questions a future in him being a key player, but says with two or three signings United could be title challengers next season.
“How many of Europe's biggest clubs rely on a 6ft 4in auxiliary forward to produce their best football?” he added.
“Real Madrid don't do it. Barcelona don't do it. With two or three ambitious signings this summer - I have mentioned Gareth Bale and Edinson Cavani as priority targets previously - I still think they can challenge for the title next season.”