Spurs will be looking to keep pace with Premier League leaders Liverpool FC and Manchester City in the title race after an impressive season under Mauricio Pochettino so far.
Tottenham have amassed 48 points from 21 games in the top flight to leave Spurs six points behind Liverpool FC as both clubs look to win the Premier League title for the first time.
Manchester United, though, are on an impressive run of form following five successive victories in all competitions under interim manager Ole Gunnar Solskjaer.
The Red Devils have eased to league victories over Cardiff City, Huddersfield Town, Bournemouth and Newcastle United to breathe life into their top-four challenge.
Manchester United booked their place in the FA Cup fourth round courtesy of 2-0 win over Reading, while Spurs beat Tranmere 7-0 before a 1-0 against Spurs in the first leg of their League Cup semi-final.
Former Liverpool FC defender Lawrenson is backing Spurs to end Solskjaer’s winning run with a narrow victory over Manchester United at Wembley.
“This is a big test for United caretaker Solskjaer and it will be interesting to see whether he will be as attack-minded at Wembley as in his first five games,” Lawrenson told BBC Sport.
“It is quite possible United will not have the same amount of possession they have enjoyed in those matches – if not, they will need a different approach.
“Tottenham’s methods, meanwhile, are tried and tested.”
Lawrenson added: “There was more news about Tottenham’s stadium this week but if it is not going to be ready until March, they are better off staying at Wembley until the end of the season.
“Moving grounds mid-season is something no Premier League team has done before, let alone one that might be challenging for the title at that late stage of the campaign and also trying to progress in the Champions League.
“If Spurs can wait until the summer to move, then they should do.”
Spurs are in third place in the Premier League table and 10 points ahead of sixth-placed Manchester United.
The Lilywhites were 3-0 winners against Manchester United at Old Trafford back in August.
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