United made contact with Lucas's advisors as they expressed an interest this month, but Goal understands Spurs have won the race for his signature, with the player having arrived from the French capital to undergo a medical with Mauricio Pochettino's side on Tuesday.
Lucas has had his eye on a move for some time, having been limited to just six cameo appearances in all competitions this season.
The ex-Sao Paulo forward has not featured since coming on as a late substitute against Strasbourg in a Coupe de la Ligue tie in December, with his last Ligue 1 appearance coming in a 5-0 win over Angers in November.
The 25-year-old declared an end to his time in Paris earlier this month as he said he would be looking for a way out of the capital and showed an interest in a move to the Premier League, describing the English top flight as "the most hotly contested in the world".
Coach Unai Emery showed no concern over losing him either, as he revealed that he told the attacker to find a new club as he has no chance of regular game time.
Lucas joined PSG from Sao Paulo in January 2013 for a reported £38m and went on to win four league titles and make 229 appearances in all competitions, scoring 46 times and setting up a further 43.