Swansea manager Michael Laudrup is said to be eager to add a left-back to his squad before the transfer window closes, particularly with Neil Taylor having been ruled out for the season with a broken ankle.
Alonso's contract at the Reebok Stadium is due to expire in the summer and that had resulted in reports that Swansea were confident of securing his services.
However, the 22-year-old has insisted that he is "happy" with his Championship employers.
"I don't read anything [about transfer speculation]. My head is in Bolton and I just want to get back with Bolton to the Premier League," Alonso told the Bolton News. "As for Swansea, I have not spoken to anyone and from the club, and they haven't told me anything.
"I am happy now. The manager is doing a great job and, as I said, if we win two or three games, we will get our confidence back and the fans back.
"The rest of the season will be better and we will be in the fight to be in the Premier League."
Alonso joined Wanderers from Real Madrid in 2010.