The Bluebirds are still riding high on the glory of their play-off victory in securing promotion to Division One.
Lawrence is already planning his assault on the First Division as Sam Hammam is determined to have a team that will not just be making up the numbers next term.
The Welsh side are keen to attract players with top-flight experience to Ninian Park and Lawrence has confirmed that he has already held talks with a number of targets, although he does not expect anything to happen in the near future.
"We spent the day dealing with proposals and talking to Premiership clubs and players who are out of contract," said Lawrence.
"It is a busy time, but we are not going to dive in. When we sign somebody we have to be sure it is the right move.
"Thus, the chances of something happening within the next couple of weeks is next to nil.
"We are working hard on this, but clubs and players want to wait until the end of the month at least."
Charlton's John Robinson and Tottenham's Gary Doherty are the two latest players to be linked to the Welsh outfit.
Welsh midfielder Robinson has been handed a free transfer by The Addicks and may well relish a return to Wales, while Doherty could well find himself out of Glenn Hoddle's plans.
Lawrence is desperate to match the club's fans' ambitions with a team that will be a force in Division One and up there challenging for promotion.
