Barcelona president Sandro Rosell said on Thursday that Arsenal can expect a bid of less than 40 million if the Catalan club decides to pursue Cesc Fabregas.
Barcelona tried to bring back its former youth player during the offseason last year, but Arsenal refused to sell.
"If last summer we offered 40 million ($56.55 million) for Cesc, and since then there has been wear and tear, now he's worth less," Rosell said.
"In the case that we were interested, our offer would be reasonable. We would not go overboard."
Spain midfielder Fabregas said on Wednesday he has left any decision on his future to Arsenal, while adding that "Barca is the best team in the world and going there guarantees titles."
The Spanish champions have also been linked to Villarreal's Giuseppe Rossi and Udinese's Alexis Sanchez.
Barcelona had previously announced it had a transfer budget of about 45 million. Rosell said, if necessary, this could be increased by using funds allocated for the 2012 summer transfer market.
Speaking to the media on Thursday, Rosell also said that Barcelona will end relations with fierce rival Real Madrid if coach Jose Mourinho continues his verbal attacks on the Catalan club.
"If the limits of sportsmanship are crossed again, we will be obliged to break institutional relations," he said.
Last season, Mourinho accused Barcelona of receiving help from UEFA referees in winning the Champions League.
UEFA handed the Portuguese manager a five-match Champions League ban for his statements. Madrid will challenge the ruling before UEFA's appeals body on June 30.