The Italy international made just 10 Serie A appearances last season, but new coach Andrea Pirlo is keen to keep him at the club and rates him highly.
Juventus are expected to shed a centre-back and Pirlo would rather Cristian Romero than Rugani leave, but Rugani has substantial interest from the Premier League.
Newcastle and West Ham are both tracking Rugani with a view to a potential move but, according to Turin-based Italian daily Tuttosport, Manchester City cannot be ruled out as suitors.
Pep Guardiola has added Nathan Ake to his defensive options, but has been on the lookout for another centre-half, with the club heavily linked with Kalidou Koulibaly, Jose Gimenez and Jules Kounde.
They are claimed to be studying Rugani as a potential option and at a fee of between €20m and €25m, he could be seen as a smart buy by the Citizens.
Rugani is an experienced centre-back and has made over 100 appearances in five seasons.
The defender has been linked with a move to the Premier League in recent years, but has continued to ply his trade in Italy.