Chelsea wants to press ahead with plans for the summer transfer window despite uncertainty over who their manager will be.
Antonio Conte looks set to leave Stamford Bridge this summer, though that is yet to be confirmed.
And The Mirror report Seri is a target for the Blues have been a long-term target.
Chelsea could mount a £30million offer for the Ivorian with Barcelona, Arsenal, and Liverpool all linked to the midfielder.
Seri was close to a move to the Nou Camp last summer before Barcelona changed their minds and pulled out of the deal.
But it is thought the La Liga leaders are interested in Seri again and ready to do battle with Chelsea.
Seri has shone for Nice this season, helping them through to the last 32 of the Europa League.
Nice lie fifth in Ligue 1 though are 19 points off fourth-placed Marseille with just four games to go.
That means they cannot qualify for Europe next season, with just the top four earning a spot from the French league.
Chelsea is set for a spot in next season’s Europa League, with the Blues fifth in the Premier League.
They are five points behind Tottenham and travel to Swansea on Saturday (5.30pm).
Luis Enrique ‘Prefers Arsenal Move’ Over Chelsea
Former Barcelona manager Luis Enrique would prefer moving to Arsenal over Chelsea, according to reports.
The decorated 47-year-old has been touted as a possible replacement for Arsene Wenger, who announced last Friday that he will be stepping down from his role as Arsenal manager after 22 years in charge of the club.
Enrique is currently one of the most in-demand managers in world football after stepping down as manager of Barcelona at the end of last season and being replaced by Ernesto Valverde.
He will bring a winning mentality to whichever club he eventually joins as he has previously won two La Liga titles with Barcelona as well as a Champions League.
Enrique moving to the Gunners could be a good match as the club has Raul Sanllehi as its head of recruitment. Sanllehi and the Spaniard previously worked together at Barcelona and enjoyed a good relationship.
Other managers the Gunners have been linked with include Celtic’s Brendan Rodgers, club legend Patrick Viera, Monaco’s Leonardo Jardim and current Germany national team boss Joachim Loew.
Enrique, meanwhile, is also on the shortlist to replace current Blues manager Antonio Conte at the end of the season.
Despite having led the club to the Premier League title last season, it does not look very likely that the Italian will be at Stamford Bridge next season after a disappointing second term.
Conte also is at odds with the club’s board over their transfer policy and it is unlikely that they will give him a second chance after what has happened this season, especially as they have been harsher on managers before.
In addition to this, they are also unlikely to qualify for next seasons Champions League as they are currently in fifth place in the standings.
However, press reports suggest that Enrique would prefer a reunion with Sanllehi over moving to Stamford Bridge.