The Saints are staring down the barrel of relegation and they may struggle to keep ahold of the midfielder.
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The 19-year-old Belgian, who Chelsea also like, has stirred up a fair amount of interest following his move from Manchester City, according to the Daily Mail.
Man Utd and Arsenal join Chelsea, who are all interested in a summer move for the central midfielder.
The report also states that Borussia Dortmund's Jude Bellingham is one marquee midfield name on Erik Ten Hag’s wishlist, as well as Barcelona's Frenkie de Jong and for West Ham's Declan Rice.
Lavia, who joined Southampton from City last summer in a deal worth up to £14 million, has been a regular starter for the struggling side this campaign.
Man City have a buyback clause, worth around £40m, but it would not be able to be activated until the following year.
He joined up with the Citizens when he has aged 16- joining from Anderlecht.
His compatriot Kevin De Bruyne said of Lavia last year: “He is very good. He's been training with us since the end of last year. If he continues his development, I think he'll be a top player.”
Casemiro has earned plenty of plaudits for his form recently - but the Brazilian has praised those he is playing with.
After the club's Carabao Cup win, the veteran said: "The style of play here is different, the build-up play, the manager, the league, the club are all different," the Brazilian told United Review. "Every club has their own way of playing, the most important thing is adapting quickly, that’s what I try to do.
"I’ll say it again, it’s impossible to do it on your own. There’s the quality of my teammates. There’s Licha [Lisandro Martinez] and [Raphael] Varane – high-quality players."
