Murray starred for Poyet’s slick-passing side as they won the League One title in 2010-11.
The two then parted company as Murray was allowed to leave for free and ended up at arch rivals Crystal Palace.
But the former striker sees Poyet - who also managed today's opponents Sunderland and took them to a League Cup final - as a potential choice for Spurs should they sack Igor Tudor.
Murray told BBC Radio 5 Live that veteran Harry Redknapp could do a fire-fighter type job as Spurs battle to stay up.
But he added: “I was with Gus Poyet and he put himself forward for the job midweek.
“If you are looking for someone who is going to hang around if they go down and make it a long term project, you want that continuity so to speak, it would have to be Gus Poyet or Tim Sherwood.”
Poyet made 82 league appearances for Spurs and later returned as assistant boss to Juande Ramos, helping them win the League Cup in 2008.
He has since had a globe-trotting coaching career and was most recently in charge of Jeonbuk Hyundai Motors in South Korea, taking them to their tenth league title.
But he left in support of assistant Mauricio Taricco, who was accused of making a racist gesture and resigned in protest.
Taricco would be a popular addition to the staff among Tottenham fans were Poyet to take the top job.
Pressure mounted on Tudor after a chaotic midweek defeat at Atletico Madrid in the Champions League.
He is being assisted by former Albion skipper and coach Bruno.