Albion have told Maheta Molango to look for another club.
The out-of-favour striker will not be offered a new contract when his current three-year deal expires in the summer.
The Seagulls are hoping to get him off the wage bill before the January transfer window closes.
Assistant manager Dean White said: "He was going to go to Italy to have trials with a couple of clubs. That doesn't seem to have materialised at the moment.
"If he doesn't go before the end of January then he is here for the rest of the season. It's in his interest to get himself out playing, because his contract is up in the summer."
Molango has made only one appearance for Albion in the last two-and-a-half years, as a substitute at Carlisle in September, after scoring 12 seconds into his debut in English football at Reading in August 2004.
The Swiss-born 24-year-old has been loaned out to Oldham and Wrexham this season following temporary stints with Lincoln and Spanish club UB Conquense last season.
Meanwhile, Albion are unlikely to sign Spanish striker Iban Espadas, who was given a trial before Christmas, because he is unproven in English football.
Gary Hart has joined boss Dean Wilkins and Alex Revell on the sick list following Saturday's 1-0 home defeat by Millwall.
Kerry Mayo, suspended for the Millwall match, is expected to recover from a calf injury for Saturday's trip to Chesterfield, when skipper Dean Hammond also returns from a ban.
Adam Hinshelwood sees a specialist later this month to establish the extent of the recurring knee trouble which has kept him out since Boxing Day.
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