Defender Jack Hendry, midfielder Scott Allan, and winger Lewis Morgan come come into that bracket, with Hendry the most likely to depart, having not started a game since early October.
"Timothy's a young talent who is a full global player", Celtic manager Brendan Rodgers said on the club's website as Weah joined his new team mates at a Dubai training camp.
'The coach told me he just wants to see me playing my game, helping the team by making runs into spaces and stretching the game, ' he told the Scotsman. I'm so excited to be here.
"I am in love with Celtic so I am really happy", he told BBC Sport. I feel like the coach has a great plan for me and I think he'll help me develop as a man'.
The highly-rated 18-year-old has scored two goals in six first-team appearances for PSG, while he has also been capped eight times by the United States.
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He said he would hold talks with the 28-year-old when he returns to Glasgow at the weekend, pointing out that the player was "not on holiday". It is an awesome feeling, but I know that is not even half the work done. Players who have dealt with any types of issues, it's admitting that responsibility and knowing where you are at, really. "Hopefully, I can do the same here at Celtic".
"My father has played at Celtic before". They wanted him to go out on loan and saw Celtic as a great possibility.
The forward met with the squad met in Dubai on Tuesday as he began his stay with the club.
The eight-times capped United States global signed on Monday for the rest of the season and joined his new team-mates at their training camp in Dubai.
Brendan Rodgers aims to bolster his Celtic squad further this month after predicting a "tight" Scottish Premiership title race. Money doesn't count for anything if the player isn't in good health.