The report claims the Portugal Under-17 player was watched by Manchester United, Liverpool, Arsenal and Tottenham Hotspur while playing for his country this week - adding that the quartet have also been monitoring his progress for the Blues' Under-18s.
Quina has been trained by Chelsea since the age of 13, having arriving from Portuguese giants Benfica, but can move freely between clubs as he is only a scholar - though the Londoners would be entitled to minor solidarity payments.
The attacking midfielder cannot sign professional forms until his 17th birthday in November.
Chelsea have faced criticism for their hoarding of young players, many of whom are farmed out on loan and sold on for profit, having failed to break into the first team.
In contrast, all four of the named suitors have placed their faith in youth of late.
United have integrated academy graduates Jesse Lingard and Marcus Rashford into their starting eleven this term, while Tottenham are reaping the rewards of having done likewise with Harry Kane in the previous campaign.
Ryan Mason and Josh Onomah have also been handed opportunities by Spurs coach Mauricio Pochettino, with Hector Bellerin and Francis Coquelin emerging up the road at Arsenal over the last two seasons.
And Jurgen Klopp has also shown a willingness to give youth its chance at Liverpool, handing debuts to Kevin Stewart, Connor Randall and Sheyi Ojo this season.