The 26-year-old is believed to be ready to leave Old Trafford in search of regular first-team football having falling down the pecking order under manager Erik ten Hag.
Van de Beek featured just nine times in all competitions last season and missed the second half of the campaign due to a serious knee injury.
The Netherlands international has only scored twice in 60 games for Red Devils since joining from Ajax for £40m in 2020, and he is not regarded as one of the first names on the teamsheet when fit.
Van de Beek still has two years remaining on his contract, but it is thought that the midfielder's days on the red side of Manchester are numbered, and several clubs are believed to be monitoring his situation.
According to 90min, Scottish treble winners Celtic are among a plethora of teams including AC Milan, Inter Milan, Roma, Crystal Palace, Nottingham Forest, Wolverhampton Wanderers, Sevilla, Nice, Ajax and Feyenoord who are all interested in signing Van de Beek.
The midfielder will likely pursue a move to a new club where he will be assured of regular starts, and former Celtic boss Lennon believed a summer switch to Parkhead can help get the Dutchman's career back on track.
Asked on The Go Radio Football Show if a move to Celtic would benefit Van de Beek, Lennon said: "Possibly - his career has sort of stalled a bit. He was outstanding for Ajax the season they got to the semi-finals of the Champions League in that really good young Ajax team.
"He went to United and it didn't work out and he went on loan to Everton and that didn't work out either. So he needs a kick-start and maybe Celtic is that place for him.
"He's certainly shown he's got the pedigree and you never lose it, you just sometimes lose your confidence or your hunger and lose your way a little bit.
"Players of that calibre just need a restart and maybe he's thinking Celtic might be that place to go but I mean, there's a lot of work to be done in a deal involving that.
"He'll be on huge money, let's not beat around the bush here. Realistically, if you're talking about [Scott] McTominay, [Kieran] Tierney or Van de Beek, it'll probably be a loan and Celtic making a contribution towards the wages."
Celtic could step up their interest in Van de Beek if they agree to part way with in-demand midfielder Matt O'Riley, who is wanted by Spanish trio Real Betis, Valencia and Sevilla as well as Brighton & Hove Albion according to the Daily Mail.
Hoops captain Callum McGregor has committed his future to the Glaswegian giants after penning a new five-year contract on Monday, while Reo Hatete, David Turnbull and summer signing Odin Thiago Holm are among the other midfield options at Brendan Rodgers's disposal.