Lawrence insists the club are talking to players about moving to the Memorial Stadium but it could be weeks before they are in a position to make any announcements about new signings.
"Things are progressing and we have a clearer idea now of who we want and who we may be able to get, but we won't be in a position to do anything this week and maybe not next week either," Lawrence told the Evening Post.
"Most players are still under contract at other clubs until the end of June and it is unlikely that anything will be announced officially until things are absolutely watertight."
Rovers are known to be targeting defenders and midfielders after releasing Joe Jacobson, Ryan Green, Craig Hinton and Craig Disley at the end of last season.
Lawrence has also confirmed the Pirates are in the market for a goalkeeper to provide competition for first-choice stopper Steve Phillips.