It had been suggested that the pair would reunite with Alan "Reni" Wren and Gary "Mani" Mounfield to play 21 UK dates and possible shows in the US.
However, a spokesperson for the guitarist told NME that the rumours were "unfounded from John Squire's perspective".
He added: "John is not initiating a reunion or tour."
Squire played on the band's self-titled debut and follow-up Second Coming but left in 1996, shortly before their split.
He released one album with The Seahorses in 1997, which was followed by two solo albums before he quit the music world to focus on his career in art.
In 2006, he revealed that despite being on good terms with Reni and Mani, he still does not speak to Brown.