He has turned down their €82,000-a-week offer, and the Serie A club have no plans of negotiating new contract terms.
Amidst this, Sport Mediaset claims that the Blues have agreed personal terms over a €100,000-a-week deal.
Perisic could undergo his medical in the coming weeks depending on when the Blues' takeover is complete.
The club are currently banned from signing players or renewing contracts amid the sanctions on Roman Abramovich .
Todd Boehly's consortium are expected to takeover in the coming days which should put an end to the restrictions.
Perisic at 33 won't be a long-term signing for Chelsea , but he would provide adequate cover in the left wing-back role.
With Marcos Alonso pushing for an exit, Perisic could compete with Ben Chilwell for a starting position next season.
Perisic, who won the Scudetto with Inter last year, has registered nine goals and eight assists in all competitions this season.