The Expressen newspaper reports that Ibrahimovic is now at his home in Malmö in southern Sweden after leaving Inter's training camp in the United States.
"He's left to go sign," Inter Milan spokesperson Luigi Crippa told the newspaper.
Ibrahimovic sudden departure from Inter comes on the heels of news that Cameroon striker Samuel Eto'o had agreed to the terms of his transfer to Inter Milan following three days of negotiations.
Concluding a deal for Eto'o's tranfer to the Serie A club was seen as a prerequisite to the consummation of the Swedish striker's move to Barcelona.
On Thursday, Jose Maria Mesalles, Eto'o's agent, emerged from two hours of talks with Inter representatives to tell the waiting press that a deal had been agreed, which was later confirmed by Inter's transfer specialist Marco Branca.
"The only problem is his loyalty bonus with Barcelona," said Mesalles.
Eto'o is due to arrive in Milan on either Monday or Tuesday to put pen to paper.
"It was a really long negotiation but it was always conducted with respect and for that I have to thank Inter," said Mesalles.
As well as Eto'o, the Catalans would pay the Italians €50 million ($71.3 million) and allow Belarusian winger Alexander Hleb to go on a season-loan to the San Siro.
According to the Gazzetta dello Sport, Eto'o will sign a five-year deal worth between €10-10.5 million a year.
The 28-year-old Eto'o, who joined the Catalan side in 2004, has a year left in his contract with Barcelona. He was the club's top scorer in the Spanish league last season, with 30 goals.
Inter president Massimo Moratti told the club's website that the transfer was "nearly finalized" and said he would not comment more until it has been completed.
But Moratti moved to deny speculation in the Italian press that Inter coach Jose Mourinho doesn't want the Cameroon star at the club.
"That's completely untrue, I've spoken with Mourinho on the telephone and he has been a part of this process all along," said Moratti.
"As for the Ibrahimovic question, that was something that he (Mourinho) always knew might happen. Obviously the coach made it clear he didn't believe the Swedish striker could go to another club but he is a big admirer of Eto'o and he is very satisfied and happy about this possibility, this exchange."
Ibrahimovic was the top scorer in Serie A last season and has been Inter's best player since joining the club in 2006 when Juventus were demoted to Serie B for match-fixing.
But while he has often dazzled on the Serie A stage, scoring some spectacular goals, he has been much criticized for failing to produce on the biggest stages, such as the Champions League.
He has also made it clear that he is not happy at Inter's failure to mount a serious Champions League challenge having been knocked out in the second round in each of the last three seasons, by Valencia, Liverpool and then Manchester United.
Meanwhile, Barcelona striker Thierry Henry said on Thursday he was looking forward to playing alongside Ibrahimovic.
"Technically he can keep whatever ball you throw at him," Henry said.
"And what I like about him is his character. For some people it is a bit too much but I don't mind. To be a player like that you have to have it."
Barcelona coach Josep Guardiola had already admitted that it would be better if Eto'o left.
"I fully understand that people ask why. He is a wonderful player. Everyone knows there are no 'football' reasons. So why? It is a question of feeling," Guardiola said earlier this week.
"I feel that it is the best for the team, for the club, but I don't dare say that it is best for Samuel. I am very grateful to Samuel, not for this year but for the five years he has spent here.
"The coach's job is not to change the personality of players but it is my job to decide who to work with. It's my responsibility and I think we need to change something."
According to Ibrahimovic's agent Mino Raiola, the Swedish star is in Sweden to spend time with his family and "participate in negotiations at a distance".
He told Expressen that he expects the transfer to be completed "within days".