"For me, he could do the kind of job that Jack Charlton did with the Republic.
"At that stage (on Friday), he hadn't been contacted by anybody about the Republic job although Terry does keep his cards quite close to his chest.
"But we had a few discussions recently about Irish players and in particular he asked me about the Reading boys (Kevin Doyle, Stephen Hunt and Shane Long).
"I see a lot of games so he would get my opinion on players."
Buxton is highly respected in the football world and also worked as part of Sven-Goran Eriksson's England set-up as a scout.
Weekend reports claimed that Venables had emerged as the main candidate to succeed Steve Staunton.
However, Football Association of Ireland chief executive John Delaney refused to comment on the issue after Sunday's World Cup draw in South Africa.
Venables lost his job as England assistant last week following Steve McClaren's sacking.
Gerard Houllier and David O'Leary have also been linked with the Republic job while Graeme Souness and Philippe Troussier have publicly expressed interest in the role.