The 30-year-old has plenty of experience to offer interested clubs should he leave the Mestalla Stadium.
Juventus and Benfica are also looking at Garay, according to Spanish outlet Super Deporte.
And representatives from the four clubs were all in attendance for Valencia’s 1-0 La Liga win over Las Palmas on Friday.
United sent top scout Javier Ribalta, chief Spanish scout Carlos Ruiz and other representative to the game.
It is said Garay would have been of most interest to the Red Devils.
Gareth Bale – Real Madrid – 14/1 (BetStars)
“Garay may be pursued as cover with Manchester United back in the Champions League”
And the unusual greater presence of scouts from United suggests they could be seriously thinking of moving for the centre-half.
Jose Mourinho has already admitted summer signing Victor Lindelof needs time to adapt at Old Trafford.
Chris Smalling could also yet leave before next Thursday’s deadline with West Brom circling.
And Garay may be pursued as cover with Manchester United back in the Champions League.
Spurs, meanwhile, have struggled to strengthen in the transfer window.
A deal worth £42m has now been agreed with Ajax for Davinson Sanchez.
And Paris St-Gemain’s Serge Aurier is also wanted as Spurs look to further bolster their backline.
With Kevin Wimmer likely to leave too, Spurs could challenge United for Garay.
But they may face competition from their European rivals who were in attendance at the Mestalla Stadium too.