The 21-year-old has been linked with a £7 million move to Tottenham.
Speculation is rife that Spurs' South-America based scouts have been monitoring the 21-year-old's progress in Brazil amid suggestions that he could be the next Paul Pogba.
The Mirror reported earlier this month that Walace - also reportedly being tracked by Sevilla, Valencia and Napoli - was rated at around £7 million by the Brazilian outfit, but club president Bolzan has insisted that he has received no offer from any club for the young midfielder.
“Walace is a player who we will not sell. It is absolutely certain," he said via Globo Esporte.
"We have a squad situation, we want to go through in the championships we're playing. It’s essential that he stays with us until the end of the year. I have no offers."
It remains to be seen if Tottenham are genuinely interested or whether this is something coughed up by the rumour mill.
With Eric Dier, Mousa Dembele and Dele Alli, manager Mauricio Pochettino arguably boasts the best midfield in the Premier League - and they are all young enough to dominate for many years.
If true, Walace would surely have no reservations about joining the Lilywhites, who have looked superb in a season which might well end with winning the Premier League title.