The 25-year-old Brazilian full-back has enjoyed an impressive debut season in La Liga, and has also been linked with moves to Valencia and Atletico Madrid.
Red Devils boss Sir Alex Ferguson is believed to be in the market for further defensive reinforcements come June, with speculation suggesting stand-in skipper Patrice Evra could leave Old Trafford at the end of the current campaign.
Brazilian brothers Rafael and Fabio Da Silva have also failed to develop as quickly as had been anticipated with the reigning Premier League champions, leading to rumours that Ferguson is ready to turn to their compatriot Siqueira.
Manchester United chief scout Martin Ferguson was spotted in the stands for Granada's 3-0 home defeat to Sevilla last Monday, with the former Udinese man thought to be his primary focus.
Having also been linked with Lille right-back Mathieu Debuchy, it is not yet clear who the club will make a move for, but expect activity when the transfer window reopens this summer.