The 25-year-old has been heavily linked with a move away from the Etihad, which has escalated since Pep Guardiola's side announced the arrival of Erling Braut Haaland from Borussia Dortmund.
Jesus has scored 13 goals and provided 12 assists in 41 appearances for Man City this season, but he was only given 21 starts in the side's Premier League-winning campaign.
The Telegraph reports that Antonio Conte's side will go head-to-head with North London rivals Arsenal to secure the signature of Jesus, who is believed to have held talks with Mikel Arteta already.
Tottenham can offer Jesus Champions League football next season, after beating the Gunners to fourth spot in the Premier League, with the Brazilian international said to be keen to remain in England.
Since arriving in Manchester from Palmeiras in 2017, Jesus has recorded 95 goals and 46 assists in 236 games for City.