Benteke, who has struggled to adapt at Anfield since joining from Aston Villa last July, looks likely to leave at the end of the season after his recent criticism of manager Jurgen Klopp.
And given the way Mourinho coaxed the best from the likes of Didier Drogba and Diego Costa during his two spells at Chelsea, Benteke could be the ideal acquisition to help restore United at the summit of English football.
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Many believed that Brendan Rodgers had signed the ideal successor to Barcelona star Luis Suarez in Benteke, but the Belgian now looks a far cry from the player that terrorised defenders during his time at Villa Park.
The 25-year-old scored the winner against Crystal Palace in early March, but his tally of eight goals from 34 appearances is his lowest since arriving in England.
Daniel Sturridge and Divock Origi are currently above him in the pecking order and he could slump further down if he remains on Merseyside with Danny Ings due to return.
Benteke will no doubt be forced to make a huge decision over his career and, though players rarely move between Liverpool and Manchester, he could buck the trend if Mourinho comes calling.
Though United fans would prefer names such as Robert Lewandowski, Zlatan Ibrahimovic and Karim Benzema to arrive, Benteke's age and undoubted potential could be unlocked by the Portuguese manager.
There is still no guarantee that Mourinho will succeed Van Gaal, yet the common consensus seems to be that he will take over if the Dutchman fails to secure Champions League football for next season.
And perhaps Benteke would be Mourinho's ideal first signing should he arrive at Old Trafford. When shown belief, the Belgian powerhouse is a proven goalscorer and one capable of reaching somewhere near the 20-goal mark - something United have lacked in recent seasons.