Kroupi, a 19-year-old born in Lorient, joined Bournemouth from his hometown club last summer for just £10 million and has repaid that fee many times over.
He has scored 11 Premier League goals this season — the first teenager to reach double figures in the division in more than two decades, matching the marks set by Robbie Fowler in 1993-94 and Robbie Keane in 1999-2000. He requires just two more goals to stand alone as the highest-scoring teenager in a single Premier League campaign.
Manchester City sporting director Hugo Viana has held talks with Kroupi's agent, with head coach Pep Guardiola described by Sky Sports journalist Sacha Tavolieri as a "big fan" of the player's technical profile.
Liverpool have been the most consistently linked club and sporting director Richard Hughes is understood to have a strong existing relationship with Bournemouth, smoothed by previous business between the clubs. Chelsea have dispatched regular scouts to the Vitality Stadium and have him high on their summer shortlist, reports The Sun.
Paris Saint-Germain and Real Madrid have also been credited with serious interest.
Bournemouth are in no rush. Kroupi is contracted long-term and the club are simultaneously in dialogue over a new improved deal, mirroring the approach taken with Antoine Semenyo before his £62.5 million move to Manchester City in January. Whether an extension changes the economics of a sale remains to be seen.
Kroupi told Téléfoot earlier this year about his ambitions.
"I had dreams of winning the Ballon d'Or, of playing for the biggest clubs in the world, but they aren't really dreams anymore, rather objectives, because I know that I can make them happen."
Sources close to the player confirm he would welcome a move to a top club this summer.