A Tottenham spokesman said: "Andy Reid is a player we admire but we have not made an offer for him."
Spurs had supposedly offered £3m on Monday even after January's £5m bid plus Rohan Ricketts was turned down by Forest chairman Nigel Doughty.
The London club already has a strong Irish contingent with the likes of Robbie Keane, Stephen Carr and Gary Doherty and ironically face the Reds in a pre-season friendly at the City Ground on Saturday 31 July.