Sevilla sporting director Monchi told a farewell news conference on Friday that Roma are among the clubs who could move for him.
On Thursday, Sevilla announced that they had reached agreement to part company with Monchi after 29 years.
The 48-year-old confirmed a report in Italy that he had met Roma president James Pallotta.
He told reporters: "It's true that I listened to their project, but that was all. I have not signed anything with anyone.
"It's true that Roma is one of the clubs that has shown the most interest in me, but I have other offers."
Comienza la rueda de prensa de @leonsfdo y José Castro,síguela en directo en #SFCTV y #SFCRadio
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- Sevilla Fútbol Club (@SevillaFC) March 31, 2017
Sevilla president Pepe Castro had hoped to keep Monchi and offered him a lucrative deal to remain.
"We've done the possible and the impossible for Monchi to remain with us," he said. "We made an offer to him that was beyond our limits.
"But in the end, we've had to consider the man before the professional. He had made it very clear that he wanted to leave."
He added that Sevilla's "doors will always be open to him."
Monchi said his decision to leave the club he joined as a player in 1988 was made because he wanted a new challenge.
"It's not a professional decision but a personal one," he said. "It's 29 years in this home, 17 as sporting director, and I'm exhausted. I need a change."
The former Sevilla goalkeeper has been instrumental in the team's success and the club's transition to financial stability.
They have won nine trophies, including five Europa League titles, since he became sporting director in 2000 with the club in the Segunda Division.
Sevilla, who ruled out Monchi's departure last summer unless they received €10 million in compensation, have agreed to let him go as free agent.
"Monchi will not have to pay a clause because, through the work he has done and the revenue he has generated for the club, he has earned that freedom," Castro said.
"Last year was not his time to go, and that is why we didn't give him that option."
Asked about the timing, with Sevilla third in La Liga and fighting to qualify for the Champions League, Monchi said: "It's never a good time. I accept that people may not approve.
"I've told the players that the best tribute they can give me is to win our last 10 league games."
He kept open the possibility of a return, adding: "I don't know what will happen in the future, but if the club calls me back and I feel refreshed I will return in any capacity they want."
Monchi has asked for a farewell ceremony to take place at the Sanchez Pizjuan stadium ahead of the game against Deportivo La Coruna on April 8.