Albion have offered Alexis Nicolas a permanent move from Chelsea and Dean Hammond a contract until the end of next season.
Manager Mark McGhee wants the 21-year-old midfield prospects to be part of the Seagulls' long-term future.
The Argus revealed in August McGhee's desire to keep hold of Nicolas, a Cypriot under-21 international.
His three-month loan does not finish until the end of October, but McGhee hopes to conclude a permanent deal by Saturday's home game against Sheffield United.
"We have made a permanent offer to Alexis," McGhee said today. "I spoke to him yesterday and we hope to resolve something before the end of this week."
Hammond, whose three-month contract expires on Thursday, has been offered terms through to the summer of 2006 instead of just for the rest of this season.
"I think he has done well enough," said McGhee. "During that spell when he was on trial almost his attitude was first class, so I have got total trust in him.
"He's got to get more powerful and harder in a sense, so he has got work to do, but I think it takes the pressure off him knowing he has got that extra year."
Hastings youngster Hammond and Nicolas, an ever-present so far this season, have played together during Albion's recent run of three wins and a draw from six matches.
Hammond is poised to continue in a right-sided role at Nottingham Forest tomorrow night as the Seagulls welcome back veteran central defender Guy Butters from a two-match absence with a calf injury.
McGhee wants Butters to combat the aerial threat of Gareth Taylor after watching Forest's first win of the season at home to West Ham on Sunday, when they came from behind with two late goals.
"Butts is looking as if he will be okay," McGhee said. "He trained yesterday and I think he will be fine.
"The strongest part of the Forest team while they were going through their poor spell was Taylor's strength in the air.
"I think we need somebody who can cope with that, particularly if they are going to play three up front. Guy is best suited to that, so we will be glad to have him back."
Adam Hinshelwood is likely to fill in at rightback after Adam El-Abd was stretchered off with damaged ankle ligaments during the second half of Saturday's 1-0 victory at Gillingham.
El-Abd was initially expected to be out for up to six weeks, but the injury is less serious than first feared and his lay-off could now be only half that long.
McGhee said: "It's a sickener. He's been getting stronger, but Malcolm Stuart (physio) thinks it is not as bad as first feared.
"He is talking about three weeks, so the fact that we have two games this week and then a two-week break means he might not miss too much."
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