The 20-year-old right-back has impressed in two games for the leaders since Spurs boss Harry Redknapp allowed him to move across London on an initial month-long deal.
"I'd like to stay and hopefully that will happen," Walker told the Kilburn Times.
"I'm enjoying it here and hope it continues. It's only a month at the moment and a case of waiting to see if it's extended.
"Harry Redknapp said he wanted me to go and play some games. It's vital for my experience and after that I'll hopefully get into the team at Tottenham.
"It's been a great move for me because I've gone straight into a winning team that plays good football."