The First Division side have lodged a £600,000 offer for the Republic of Ireland international but Spurs have been holding out for £1m.
Lawrence said: "The lad wants to come down and it's now up to Spurs. But this transfer must be done this week and before international players go off for 12 days with their national teams. It's better to strengthen your squad when you are playing well and Gary will do that for us."
Doherty is included in the Spurs squad for tonight's game at Liverpool, although he is unlikely to play.
Darren Anderton returns to the squad following his Achilles problem but there is no place for South African skipper Mbulelo Mabizela, who played 90 minutes in the reserve team's 2-1 defeat by Fulham last night.
Meanwhile, Gerard Houllier stood up to his critics today, saying: "No one is going to tell me how to do my job. I don't tell others how to do theirs, so I should be given some credit for knowing how to do mine."
Liverpool's manager has been criticised over his use of £5m summer signing Harry Kewell.
The left-footed winger may have looked out of place on the right flank but Houllier said: "He is new to the team and sometimes it takes a bit of time to settle in. I was not surprised that he did not start very well against Aston Villa on Sunday. But he got better as the game went on and made a good contribution. He is a big player, a winner and fighter with creative talent."
Liverpool defender Markus Babbel today joined Blackburn on loan for the season.
