French media outlet L’Equipe, as quoted by talkSPORT, is reporting that both Manchester clubs have cemented their interest in the teenager.
The same article states that the 17-year-old has been likened to Manchester United record signing Paul Pogba following a series of impressive performances at Sochaux.
According to the same story, Everton are also interested in Agoume, while La Liga leaders FC Barcelona are monitoring the French prospect.
Agoume is thought to have less than 18 months left to run on his current deal with Sochaux to raise questions about his long-term future at the Ligue 2 side.
Sochaux are embroiled in a relegation battle with possible demotion to the third tier of French football on the cards.
Agoume was 16 when the French youngster made his Ligue 2 debut in a 2-1 victory over Troyes back in October.
The highly-rated midfielder has gone on to make a further 13 appearances in all competitions over the past five months or so.
Manchester United were 3-1 winners against Ligue 1 winners Paris Saint-Germain in the second leg of their Champions League round of 16 clash last week.
The Red Devils were joined in the quarter-final draw by Tottenham Hotspur, who were 4-0 aggregate winners against Borussia Dortmund.
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