West Brom have joined the race to sign Gueye, along with West Ham, Southampton and Crystal Palace.
A highly-rated Senegalese international, Gueye, 25, has played for Lille since 2008, making his first-team debut in 2010.
He was a key figure in their plans during the 2014/15 campaign, scoring four goals and registering three assists in 44 games across all competitions, and showing off his box-to-box ability that has never been present before.
Naturally a defensive midfielder, Gueye added an attacking threat to his game, and utilised his impressive physicality to great effect by developing into one of the best all-round midfielders in Ligue 1.
His impressive form has seen much interest in him over the last few weeks, with France Football claiming Southampton want to sign him, whilst West Ham and Crystal Palace have also been linked with making a move this summer, as per a Mail report.
West Brom have now entered the race to sign him, and the France Football report claims he has a €10 million asking price on his head.
If any club can agree a deal with Gueye, he looks to be a great signing for the Premier League, and he could prove to a be a real budget piece of business for whichever club wins the race for his signature.