Daniel Gay, Darryl Flahavan, Leon Cort, Damon Searle, Stuart Thurgood, Kevin Maher and David McSweeney are all currently mulling over offers, and the club are growing impatient.
"I have given them until the end of next week, when I want a final decision," said Shrimpers boss Rob Newman.
McSweeney is due to sign his contract this weekend, but their remains a question mark over the other six.
Flahavan is being eyed by Brighton, while Maher has been the subject of a bid from Leyton Orient.
Left back Searle is also attracting major interest with Hull, Oxford and former club Stockport all monitoring his situation.
