The Portuguese star has been a revelation since joining in the summer on a season-long loan deal from Benfica.
As part of the deal, Celtic have first option to make the move permanent with a reported fee of £6million.
According to the Daily Record, talks between Celtic and Benfica are progressing with the move and could be completed in the coming days.
The 22-year-old has been back in Portugal receiving treatment for an injury which kept him out of the last seven matches.
In his 18 games for the club Jota has managed to score eight and set up a further six. He has excited fans with his wing play and his ability to go past players on either side.
Meanwhile, Celtic have been linked with Australian international Riley McGree.
Ange Postecoglou knows the player well from his time as Australia boss.