Albion will not be offering Argentinian free agent Emmanuel Ledesma a contract.
The former QPR attacker featured in a friendly win at Fulham on Tuesday but will not be kept on.
Boss Gus Poyet said: “He has plenty of quality and a great left foot but he would not be likely to start and we do not need to bring in cover for the positions he would play.
“That would be up front or to the left of attack and we have options in those positions.”
Striker Glenn Murray suffered a twisted ankle this week but is likely to train today as preparations for Hartlepool’s visit on Saturday continue.
Hartlepool’s play-off hopes, which flickered around Christmas, have been dampened by 4-0 defeats in their last two away games, at Peterborough and Oldham.
They have also been thumped 3-0 at Notts County and gone out of the FA Cup 4-1 at Watford since the turn of the year.
Poyet, though, does not anticipate an easy time at Withdean.
He said: “I expect Hartlepool to be very organised and difficult to beat, doing the job they normally do.
“Before the two 4-0s they drew 0-0 at Bristol Rovers and were difficult to beat. They had a very good December, then a bad January.”
Albion are three points clear with games in hand but, once Saturday’s games are completed, second-placed Bournemouth will play twice before the Seagulls are next in League action.
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