Alonso is out of contract at the Reebok Stadium in the summer and yet to agree a new deal with the Trotters despite being offered an extension.
Fiorentina are thought to be frontrunners for his signature, while Stoke and Celtic have also been linked with the 22-year-old former Real Madrid youngster.
Alonso's father and agent, Marcos Alonso Pena, says a move to Serie A with the Viola at the end of the campaign is a likely option for the defender.
But Alonso senior insists assisting Bolton's promotion push is his son's main priority at the moment.
He told tuttomercatoweb of the youngster, who joined the Trotters from Real in 2010: "Yes, Fiorentina are very, very close to Marcos.
"We were in Florence for the first time in December, to speak with the Viola.
"But now Marcos wants to finish this season quietly with Bolton, trying to do his best professional job to bring the club into the Premier League."