Celtic manager Brendan Rodgers earmarked a new contract for Greg Taylor as a "priority" following the end of the transfer window.
Rodgers got the additions he was looking for by the time the window closed, including on-loan Barcelona left-back Alex Valle.
And now he hopes the club can reach an agreement with Taylor, who has entered the final season of his current deal.
The 26-year-old is on course to reach 200 Celtic appearances around the turn of the year after making the left-back position his own since arriving from Kilmarnock five years ago.
But Rodgers admitted there was "no update" on the contract situation.
"I really hope that we can get something organised on that," he said ahead of Saturday's Premiership encounter with Hearts at Celtic Park.
"He's a fantastic player for us. How he makes that position work how we want it to look, he's first class.
"He knows we really want him to stay and hopefully between his representatives and the club we can organise that because he is a player that I really rate.
"I have seen him grow here from the outside looking in and obviously having the chance to work with him now for over a season.
"I really like everything about Greg. I love his personality, I love his spirit, I love how he plays the game of course.
"He plays the game like a midfield player coming from that outside position in, so he really makes it difficult for the opposition. Technically strong. For what you'd say small in stature he competes in his duels, he wins headers.
"He does a lot of really, really good things in the game which I really like and really appreciate.
"So I really hope that we can tie him down. In this period now he would be a real priority for us to try and get something sorted."
Rodgers was not aware of any imminent news about a contract extension for another full-back, Alistair Johnston, amid reports the club were set to offer him a new deal to bring his wages in line with other players.
"Nothing that I am aware of," Rodgers said. "I would love to have him here as long as we can. He's got three and a half years left on his deal and he is playing ever so well.
"I think now you see he has his power, his strength and his running ability and he's in a really good place.
"So of course naturally as a manager you'd want him to be here but that's something between his representatives and the club really."
The Canada right-back trained on Friday after returning home early from international duty because of tightness in his leg, while Taylor and James Forrest are also fit after pulling out of the Scotland squad.
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