Spurs are currently on the lookout for a new manager after dismissing Jose Mourinho in April prior to their League Cup final - which they lost 1-0 to Manchester City - replacing him temporarily with Ryan Mason until the end of the season.
The North London club have already suffered setbacks in their search for a new manager, with targets Julian Nagelsmann and Brendan Rodgers turning them down, and hence Murphy has encouraged Tottenham to consider Potter.
Speaking to talkSPORT, the former Tottenham midfielder said: "Tottenham fans generally want someone who has been there and done it before, but they've just gone down that road and it didn't work. So I'm not surprised he [Potter] is linked with the job, but we'll have to wait and see.
"Similarly we were talking off air about when Tottenham brought in [Mauricio] Pochettino. He'd only been at Southampton for five minutes before they took him. So they could go down that route again. It might surprise one or two."
Potter has managed to keep Brighton in the Premier League for the last two seasons since replacing Chris Hughton in 2019.