Lambert joked to BBC Essex: "I think Hibs want about £20m for him, so we'll get to about 19 and hopefully he'll do it."
Colchester assistant manager Ian Culverhouse had told BBC Essex they were looking to strengthen the squad in some areas.
"Paul's spoken to a lot of people and, although things have been a bit a slow, we are hopeful that, in the next couple of weeks, it will come out," he said.
Culverhouse suggested other club's reluctance to sell during the current January transfer window was making progress slow going.
"The chairman wants to back us as much as he can, but he isn't going to pay silly money for people, that's for sure," he explained.
"The manager has recognised where we need strengthening and bids have been put in, but the clubs at the moment are not forthcoming."
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