The Spanish left-back has been out of action since breaking a foot in August, but his latest scan showed the bone has healed.
And the 20-year-old will now step up his comeback with a reserve-team outing in the coming weeks.
He told the Bolton News: "I am doing all I can to get back as soon as possible. The scan came out all clear and the doctor said I am making really good progress.
"I have started running now and hopefully I will be back in full training with the squad in one to two weeks.
Alonso will be followed back in due course by fellow defender Sam Ricketts - out since February with a ruptured Achilles - but boss Owen Coyle said: "Sam is getting closer but there is no sense rushing him."
Source: Team Talk
Source: Team Talk