Harry Redknapp's relegation-threatened QPR had been linked with the centre-back after struggling to complete a deal for West Bromwich Albion's Jonas Olsson.
But O'Neill is in the dark about the rumours despite Bramble being in the last six months of his contract.
"I do not know anything about Titus going to QPR," O'Neill said in the Sunderland Echo.
"It is only speculation and no-one has spoken to me about it."
Bramble has also been linked with former club Ipswich Town, having suffered from a series of injuries and off-field problems over recent years which mean he is likely to be released by Sunderland.