Inter president Massimo Moratti joked to a group of school children last weekend that he would sign the mercurial Argentine as a present for them in January.
However, Saturday's Gazzetta dello Sport quoted him as saying: "On Sunday I was joking, but now we'll see."
Inter coach Rafael Benitez was also in a playful mood in a news conference ahead of Sunday's Serie A game at Cagliari.
"If the president wants to do something with Messi, I certainly wouldn't oppose it," the Spaniard said smiling.
He sounded more serious though when asked again.
"If the president wants to take Messi, I would not say no."
Messi, 23, has spent his career at Barca having been picked up by the Catalans as a youngster in Argentina and has been quoted as saying he wants to stay at the Nou Camp for good.
The World Player of the Year has a contract with Barca until 2016 which includes a 250 million euros buyout clause.
Treble winners Inter did not invest in players in the close season with Moratti saying he would buy in January if needed.
Benitez played down potential moves for Real Madrid pair Karim Benzema and Kaka, who has also been linked in the media with former club AC Milan despite chief executive Adriano Galliani saying a return would be difficult.
The Inter boss was also asked about the sale of his former club Liverpool to New England Sports Ventures.
"I respect my former team's fans and I wish them all the best but I prefer not to say too much, maybe I will in the future," added Benitez, who also had words of support for Inter midfielder Dejan Stankovic.
The Serbia captain made various hand gestures to his country's fans as they rioted and caused the abandonment of Tuesday's Euro 2012 qualifier in Italy.
"I talked a bit with Stankovic, no one liked what happened. Dejan wanted to help to calm things down but everyone agrees that it wasn't an easy situation to manage," Benitez said.
