The Portuguese winger has been a revelation for the Hoops since joining on loan from Benfica in the summer and it is believed negotiations started well with his parent club over the weekend.
The Daily Record suggest a £6million deal to keep him at Parkhead on a permanent basis is close to being finalised.
Jota has scored eight goals and provided seven assists in 18 appearances for the clubs but his progress has been halted in recent weeks by a hamstring injury.
Meanwhile, Serie A outfit Udinese are set to return with a second offer for defender Stephen Welsh after the Italian side had an initial loan bid until the end of the season, with an option to buy, knocked back by the Hoops board.
Manager Ange Postecoglou is in no rush to sell the highly-rated 21-year-old centre-back, who still has four years remaining on his Parkhead contract.
Welsh has featured 19 times and scored two goals so far this season.
However, with Christopher Jullien back in full training and due to return from a long-term knee injury later this month, it is feared Welsh’s game-time could be restricted during the second half of the season with Cameron Carter-Vickers and Carl Starfelt also competing for a starting spot.
Italian media outlet Messaggero Veneto claim that Celtic have started the bidding at £1.6million (€2million) for Welsh.
He played a major role in the club’s Europa League campaign this season and scored in the 3-2 victory over Real Betis in December.
Udinese remain keen to secure Welsh’s services but they will face a battle to land him.