The 20-year-old club has impressed during his brief stint with the Premier League club and his agent, Warren Craig, is hopeful of securing a dream move to England.
"Mat has done well this week at Spurs and the feedback he has received has been very positive," Craig told AAP.
"His trial will finish tomorrow [Friday] and then we will discuss with the club if they wish to take things further."
Ryan has further trials lined up with West Brom and Wigan after his time at White Hart Lane.
The Central Coast Mariners custodian was named A-League's best goalkeeper last season and is one of Australia's brightest prospects.