The Scottish champions have been in talks with AC Milan over loaning Laxalt and are pushing to get a deal over the line before the transfer window closes.
Laxalt is now being put through his medical paces in London and if he passes the tests without an issue he is expected to then travel to Glasgow later.
The left-sided player will then put pen to paper on a loan contract with Celtic.
The Bhoys have been looking to put a purchase option into the loan agreement in the event he impresses in Scotland.
It is unclear whether they have reached an agreement with AC Milan over the size of the purchase option as it had been an area of discussion.
The 27-year-old operates as a left-back, but can also play further along the left side.
He has another two years left to run on his contract at the San Siro.