Tottenham Hotspur have approached Manchester City about signing Savinho, with talks under way between the two Champions League clubs.
City, however, do not want to sell the 21-year-old who only signed for them last summer from sister club Troyes.
Spurs have been in the market for a number 10, and that search is intensifying after a long-term injury to James Maddison.
Savinho can play at No 10 but is predominantly a winger.
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Sky Sports to show 215 live Premier League games this season
Spurs winger Dejan Kulusevski has previously played at No 10 when Maddison has been injured.
Savinho scored three goals and provided 13 assists in 48 appearances for Man City last season.
The Brazil international came on as a half-time substitute in Saturday's 3-0 pre-season win over Palermo.
Savinho may find game time harder to come by at City this season following the arrival of Rayan Cherki, while he faces competition from the likes of Phil Foden, Oscar Bobb and Jeremy Doku.
Tottenham, meanwhile, are pursuing a deal for Savinho, having spent £120.3m this summer on six signings.
The Europa League winners turned Kevin Danso's (£20.9m) and Mathys Tel's (£29.9m) loan moves into permanent deals.
Mohammed Kudus has been their most expensive signing of the summer so far after his £55m arrival from West Ham.
Midfielder Joao Palhiha has joined on loan from Bayern Munich, while defenders Luka Vuskovic (£9.5m) and Kota Takai (£5m) have also joined the club this summer.
Sky Sports to show 215 live Premier League games this season
From this season, Sky Sports' Premier League coverage will increase from 128 matches to at least 215 games exclusively live.
And 80 per cent of all televised Premier League games this season will be on Sky Sports.