Spurs have been in fine form in recent weeks and have won their last four games on the spin in the top flight.
The north London side also booked their place in the League Cup semi-finals last week with a 2-0 win at local rivals Arsenal.
The Lilywhites – who beat Everton 6-2 at the weekend – will be aiming to keep up the pressure on the Premier League’s top two on Boxing Day when they host Bournemouth at Wembley on Wednesday.
And former Liverpool FC star Lawrenson is tipping the Lilywhites to claim all three points when they host the Cherries in north London.
Writing in his column for BBC Sport, Lawrenson said: “The great thing for Tottenham after they beat Everton 6-2 was that nobody asked Mauricio Pochettino afterwards about going to United – the questions were all about whether Spurs can win the league.
“We already knew Tottenham are a very good team with a very clever manager but it was such a good display, and the result was one of those that makes you sit up and say ‘wow’.
“Bournemouth got a good win against Brighton on Saturday but this is a different sort of test for them, and, if Spurs play at the level they can, they will win.”
Tottenham are currently in third place in the Premier League table and just six points behind leaders Liverpool FC as they look to keep themselves in the race for the title.
The Lilywhites are still aiming to win their first major trophy under Mauricio Pochettino despite their fine form in recent seasons.
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