Italian media outlet Corriere di Torino, as quoted by the Daily Express, is reporting that Matuidi is prepared to consider a switch to Manchester United in the current transfer window.
The same article states that the experienced France international is intrigued by the idea of playing in the Premier League after a long and distinguished career.
According to the same story, Ole Gunnar Solskjaer could look to sign Matuidi if Paul Pogba ends up sealing a big-money move to La Liga giants Real Madrid this summer.
The Daily Express goes on to state that Real Madrid remain confident of signing Pogba in the summer transfer window.
Manchester United have contended with speculation surrounding their World Cup winner throughout the summer after Pogba endured a difficult third season at Old Trafford.
The Red Devils failed to win a trophy for the second successive season despite Solskjaer taking over the reins from Jose Mourinho midway through the campaign.
The 20-time English champions started their summer spending with the £18m addition of Daniel James from Swansea City before Manchester United snapped up Aaron Wan-Bissaka in a £50m deal from Crystal Palace.
MORE: Man United latest news
MORE: Arsenal latest news
MORE: Chelsea latest news
MORE: Liverpool latest news