Spurs and big-spending Ligue 1 side Monaco have both indicated they are ready to rival the Old Trafford club and Brendan Rodgers' side for the former Arsenal star.
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Goal learned last month that United had made a move for the Cameroon international, while there is also strong interest in the player from Anfield boss Rodgers.
The departure of David Moyes from Old Trafford has not ended United's pursuit, with new boss Louis van Gaal aware of the need to significantly reinforce his central midfield.
United has been dealt a significant blow in its pursuit of Toni Kroos, with the Bayern Munich midfielder ruling out a move to Old Trafford.
"The club [Bayern] was very clear and told me that a transfer in 2014 would not be possible," Kroos told Bild. "There have been many speculations, but Manchester United was never an issue and is no issue right now."
But United admires Song's ability to anchor the midfield as well as fill in at center back, and is also targeting Barca's Cesc Fabregas and Sporting Lisbon star William Carvalho.
Liverpool and Spurs are both in the market for a proven Premier League midfielder, with the Londoners expecting a bid from Chelsea for Brazil international Paulinho. Atletico Madrid and AC Milan are also monitoring Song's availability.
The 26-year-old appeared in 31 of Barcelona's 59 matches in all competitions this season but struggled to cement a regular first-team spot. He is now prepared to call time on his spell at Barca even though he has three years remaining on his contract.
The Spanish giant is willing to cash in on the Cameroonian although his fee is expected to be just under 10 million euros, little more than half of the €18.5 million the club paid Arsenal for him in the summer of 2012.
Song joined Arsenal from French club Bastia as an 18-year-old and spent seven years at the Emirates Stadium, where he established himself as a key component of Arsene Wenger's midfield before following in the footsteps of Fabregas by moving to Barcelona.