Barcelona have rejected a first offer of around €40 million ($46m) from Paris Saint-Germain for Ferran Torres, a source confirmed to ESPN.
Torres, 26, communicated to Barça last week his desire to join the European champions having already reached an agreement over personal terms.
With his deal at Camp Nou due to expire in 2027, Barça are prepared to sanction an exit this summer, although they are holding out for a bigger fee.
Negotiations are expected to continue between the two clubs, the source added.
Speaking ahead of Wednesday's UEFA Super Cup clash with Aston Villa, PSG coach Luis Enrique refused to be drawn on the potential signing of Torres.
"There is no place for it [p the question]," he told a news conference on Tuesday. "I don't speak about the transfer market, I only speak about the players who are at Paris Saint-Germain."
Torres remains on holiday after scoring the winning goal in the World Cup final in July as Spain beat Argentina to win the tournament for the second time in the country's history.
He is due to return to training this week as Barça step up preparations for their LaLiga opener against Elche on Aug. 23.
In a range of interviews since winning the World Cup, Torres has made it increasingly clear that he is keen to join PSG.
He called on Barça to "show me some love" if they wanted to keep him, hinting that he had a dream destination in mind.
A source subsequently confirmed to ESPN last week that he wants to join PSG, where he would play under Luis Enrique, his former coach with the Spanish national team.
PSG are in the market for a new striker after the departure of Gonçalo Ramos to AC Milan this summer, while Randal Kolo Muani, who was on loan at Tottenham last season, has joined Juventus permanently.
Ousmane Dembélé has been used centrally, but Luis Enrique is keen to add other options to his squad ahead of the new campaign.
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Torres started his career as a winger but has been used primarily as a No.9 during the last two seasons at Barcelona.
He netted 21 times in 49 appearances last year having scored 19 goals in 45 matches in the previous campaign.
The former Manchester City man's possible exit would speed up Barça's pursuit of a striker after Robert Lewandowski joined Chicago Fire.
ESPN have previously reported that Julián Álvarez is the club's top target, although Atlético Madrid's reluctance to lose the Argentine could force them to explore other options.
Álvarez returned to training this week following his participation at the World Cup, with various reports in Spain suggesting he will ask Atlético once again to let him join Barça.
During the World Cup, he told ESPN that "a transfer would be best for all parties" and that he wanted Atlético to allow him to "fulfil his dream."
Barça lodged a bid of around €100m for Álvarez earlier this summer, but it was turned down by Atlético, who insist they will not let him leave.