Sporting CP president Frederico Varandas and sporting director Hugo Viana were in London on Friday to visit Manchester United's Mayfair office.
Varadas and Viana spent the morning and afternoon with United officials before returning to Lisbon in the evening.
United are expected to bid for the midfielder before the end of the month.
Sporting coach Silas said last night: "He is a huge player. All players like Bruno always have a lot of market. We know that he will always be a much talked about player and sought after by clubs as big as the talk.
"I don't like to think about that before, but I'm starting to think about alternatives within our team if Bruno doesn't stay with us. I hope that doesn't happen. In Portugal, unfortunately, we can't keep the best players for long. Bruno is the best player in the league."