The Blues have been strongly linked with a move to sign the 26-year-old midfielder over the last few months, as have some of Europe’s other top clubs.
Chelsea FC, though, are yet to make any new signings this summer amid the uncertainty about the managerial situation at the west London club.
Antonio Conte is widely expected to depart, with Maurizio Sarri taking over, although there has not yet been any official word from the Blues.
Seri could be set to leave Nice this summer and Sky Sports News reporter Sheth feels that a deal for him to move to Stamford Bridge could have been concluded weeks ago.
Speaking on the Sky Sports Transfer Talk podcast, Sheth said: “The uncertainty over everything happening at Chelsea…
“I wonder could a deal for Seri have been concluded if the manager situation had been sorted a few weeks ago.”
Chelsea FC finished in fifth place in the Premier League table last season under Conte as they missed out on Champions League qualification.
However, they did end the campaign on a high by beating Manchester United in the FA Cup final back in May to finish the season with a major trophy.
MORE: Man United latest news
MORE: Arsenal latest news
MORE: Chelsea latest news
MORE: Liverpool latest news