The Essex club missed out on the League One play-offs this term following a horrible run of form midway through the season.
But with Tilson now planning for a renewed assault on promotion when the new campaign kicks off, Martin is hoping that any signings can be made sooner rather than later.
"You don't just suddenly start thinking about new signings when the season comes to a close," he told his club's official website.
"It is still very early days and there haven't been any bids from us yet but we would want to get players in quicker this year because continuity is very important."
And Martin, who revealed that Tilson is currently speaking with out-of-contract skipper Peter Clarke, is also hopeful that loan duo Dorian Dervite and Theo Robinson will be at Roots Hall next season.
The pair impressed after moving from Tottenham and Watford respectively and Martin added: "It certainly isn't a definite no that we aren't going to be getting them."