The midfielder, who is currently in England with Brazil's Olympic squad, was the subject of a 35million euros (£27million) offer from United, according to an official from the Brazilian club.
The Premier League giants are reported to have dispatched a delegation to Sao Paulo last week, led by chief scout Jim Lawlor, to try and broker a deal.
An offer is reported to have been made, but the Sao Paulo say it is not enough, having already shunned approaches from Real Madrid and Inter Milan.
Director Marco Aurelio Cunha explained that they consider only Neymar would be worth more in Brazil, and with his valuation over £50millon it shows how highly Lucas is regarded by Sao Paulo.
"Manchester United made a very important offer of 35million euros but they would need to produce a little more," Cunha was quoted as saying by TMW.
"For us there is only Neymar worth more, after him is Lucas and we would not want to sell for less than this sort of value.
"For us it is still better to have a good player than lots of money in the bank."
Reports in Brazil suggested that Lawlor's delegation, as well as Sao Paulo, met Lucas' father with the permission of the club.
United, who are currently on tour in South Africa, have not yet commented on the Lucas situation, either to confirm or deny an interest.
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