According to the Mirror, the two Premier League outfits are monitoring his contract situation at the north London club. Mauricio Pochettino signed the Kenyan international from Southampton, with Wanyama playing under him for the Saints in the 2013/14 season.
The Argentine coach left the south coast club to take the managerial role at Spurs in the summer of 2014, and two years later, his former player followed him to Tottenham, where he signed a five-year deal at the club. Wanyama still has three years left on his current contract, which will run down in 2021.
He put in impressive performances for Tottenham in his first season with the club. However, the 26-year-old picked up a knee injury during pre-season last year, forcing him to spend time on the sidelines for the majority of the first half of this campaign.
The African star told the Daily Mail, as quoted by the Evening Standard, that it was the "lowest point" of his career.
"This has been a dark time for me. When Tottenham played Real Madrid at Wembley and I had to watch... I wanted to play so badly, it was probably the lowest point of my career," Wanyama said.
Since making his returning from injury, the midfield powerhouse has seen limited action in the first team, with Pochettino carefully managing him in order to avoid any setbacks. However, this has not put off any potential suitors.
United and Liverpool are in the market as they look to replace existing players in their squads. The Red Devils are looking for a player to come in for Michael Carrick, with Marouane Fellaini's future at the club also not decided. Meanwhile, the Merseyside outfit need someone in for Emre Can, whose Anfield contract will run down in the summer.
Carrick has already announced his decision to retire after the end of the season. However, the futures of Fellaini and Can at United and Liverpool, respectively, are yet to be decided, despite the two clubs insisting that they want to hold on to their midfielders.
Jose Mourinho has publicly expressed his desire to bring in a midfielder in the summer transfer window, while Can has been heavily linked with a move to Juventus on a free transfer. The two clubs could he heading for a transfer battle for Wanyama.
However, it will be difficult for United and Liverpool to convince Tottenham chairman Daniel Levy to sanction the ex-Southampton man's sale.