The winger joined Milan on loan from Everton until the end of the season in January and he scored his first goal for the club in last week's 2-1 win over Fiorentina, capping a fine start to his Serie A career.
Deulofeu, 22, has immediately settled with Vincenzo Montella's side, but it is Barca – who maintain an option to buy the player from Everton as part of his 2015 Camp Nou exit – who will determine his long-term future in Italy.
"So far nobody from Barcelona has contacted us, but clearly his future does depend on what they want because they do have this option," Gines Carvajal, Deulofeu's representative, told Calciomercato.
"His partner is staying in Barcelona - she is pregnant and can't really travel at the moment, so their daughter will be born in Barcelona.
"But I wouldn't be so sure that [re-joining Barcelona] is going to happen.
"Right now Barcelona have other things to think about. They need to get back on their feet in LaLiga and overturn the 4-0 Champions League defeat to PSG.
"Deulofeu is very happy to be at Milan, so I certainly wouldn't rule out him pushing to remain here after the loan spell.
"We often speak and he seems almost surprised at how well he has settled in at Milan. The squad welcomed him, he likes the city, the club infrastructure and the fans.
"I was certain of Gerard's quality as he is a great player, but I did not expect him to have such a good start at Milan.
"It took a long time for him to arrive, but the determination of Rocco Maiorino, president Silvio Berlusconi and Adriano Galliani had a decisive role.
"Vincenzo Montella really wanted him and it was the right choice to make. Gerard immediately felt the confidence of him and that is fundamental to doing well."