The deal is progressing but STV Sport understands there is still work to be done for it to be finalised.
The Uruguayan international will join up with the Scottish champions on a season-long loan – if Celtic can conclude the negotiations before tonight’s midnight deadline.
Neil Lennon has been on the hunt for a left-sided defender since Boli Bolingoli left the club on loan last month.
Laxalt has been capped 24 times for Uruguay, including four appearances in the World Cup in Russia two years ago.
The 27-year-old has previously played for Inter Milan, Bologna, Empoli, Genoa and Torino, and can play as a left back, left winger and central midfielder.
He would become Lennon’s sixth summer signing after the arrivals of Mohamed Elyounoussi, Vasilis Barkas, Albian Ajeti, David Turnbull and Shane Duffy.