Southend quartet Franck Moussa, Francis Laurent, Jean-Francois Christophe and Stuart O'Keefe have all requested to leave the club.
The four players were all absent from the 2-0 friendly defeat at Dartford on Friday but, if they do move on, boss Paul Sturrock has already pledged to bring in replacements.
"All four have said they no longer want to play for Southend United," Sturrock told the club's official website. "With that in mind I didn't feel it appropriate to include them in the team at Dartford."
He added: "Their hearts wouldn't be in it which is no good to us at this moment in time as we try to get ready for the start of the season. Equally if they were to get injured that has a knock on for both the player and the club.
"If they do end up leaving then we will replace them with more new signings who want to be a part of what we are building here."
Elsewhere, Scott Spencer has missed the last three days of training with a stomach bug, while Barry Corr also missed the Dartford clash with a back problem. Sturrock added: "Barry has had his injury problems and although this is just a slight tweak we need to manage him at the moment."
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