The 24-year-old has been in and out of the side under head coach Daniel Stendel who appears to have now frozen him out of the first team squad.
The deadline for Premier League and Championship clubs to bring in players was three weeks ago but they can still loan or sell them to clubs in the lower leagues in England or in various other countries until Monday.
The Reds have, in previous windows, rejected bids from overseas clubs for Cavare. Asked what the situation is with the Frenchman, coach Chris Stern said: “It’s a good question. I do not have an answer. I am probably not the right person to talk about it.”
Barnsley could also send players out on loan. Striker Victor Adeboyejo is yet to score in seven games on loan to League One Bristol Rovers. Another striker, George Miller, joined League Two Scunthorpe United for the season last week and played the full 90 minutes of their 1-0 loss at Macclesfield Town on Saturday.
The other players who could be loaned out are those on the fringes of the squad. They include winger Dylan Mottley-Henry and central midfielder Jared Bird, who have both not played a league game since the 2017/18 Championship campaign. Goalkeeper Jack Walton has not been in a matchday squad this season but may be needed on the bench now Sami Radlinger is injured.
Stern said: “At the minute, we have injured players and, if we keep loaning players, it makes the group even smaller. We may need all the players.”