Both teams have been on the lookout for new midfielder this summer, with Seri linked with a switch to England for well over a year after previously drawing interest from Manchester United and Manchester City.
Newly promoted Fulham have also been named as a potential destination for the Ivorian, though it's thought that a move to Craven Cottage is not his preferred option.
Arsenal have seen Santi Cazorla and Jack Wilshere depart this summer, and new manager Unai Emery and chief recruiter Sven Mislintat have been busy in the transfer market.
Uruguayan international Lucas Torreira will soon complete his move from Sampdoria after getting knocked out of the World Cup, but it has been suggested that Seri could well be the perfect complement in a tenacious new Gunners team.
Chelsea are yet to make any summer signings as things stand. That has a lot to do with their managerial situation, with Antonio Conte remaining in charge following a failure to so far release Maurizio Sarri from his contract at Napoli, despite the Serie A side already hiring a replacement.
Earlier this summer it was rumoured that Seri was having doubts about joining Chelsea because of the uncertainty over which coach he would be playing for. At the time, the same was said to apply to Bayern Munich striker Robert Lewandowski.