With Neil Sullivan set for a move to Chelsea, Spurs need another goalkeeper to put pressure on current number one Kasey Keller.
Robinson looked set for moves to Arsenal or Manchester United during the summer, but they never materialised.
He also appeared to be on his way out of Elland Road when Leeds agreed a £3m fee with Aston Villa but the deal collapsed when Robinson failed to agree personal terms.
But Tottenham are among those clubs who feel they can take advantage of Leeds financial situation to prise England international Robinson away.
Robinson's representatives SEM are making no comment on the speculation.