The 23-year-old custodian, who is under contract to Canadian club Calgary Storm, has had similar trials over the last few weeks with Division One sides Portsmouth and Wolves.
Hirschfeld is keen to try and latch on with a European-based club, after an impressive display for his country during the Concacaf Gold Cup in January, where he was named top goalkeeper in the 2002 edition of the confederation's championship
The Canadian has had trials with Scottish Premier League side Hearts and Division One club Barnsley, and was involved with German Bundesliga side Energie Cottbus.
He spent last summer playing on loan with the Vancouver Whitecaps but he is looking to make a big move to a higher profile club.
Glenn Hoddle's side already have Scotland number one Neil Sullivan, American international Kasey Keller, and 20-year-old Irish custodian Gavin Kelly on their goalkeeping roster.
Keller out-duelled Hirschfeld in goal during a penalty shoot-out at the Gold Cup, when the United States dethroned Canada as title holders in the semi-finals.
Calgary Storm manager and director of football Thomas Niendorf said: "The goal for Lars is to try out for the (Spurs) third goalie position.
"It would basically be an apprenticeship for him for the next one or two years.
"They (Spurs) are looking to bring in a third goalie to develop as a professional prospect."
Hirschfeld may see action for Spurs' reserves against arch-rivals Arsenal on Thursday.
Niendorf added: "He feels very comfortable. I talked to him today and he had two very good training sessions.
"He feels they are making a very serious effort to look at him."
(Picture courtesy of the Calgary Storm official website - www.calgarystorm.com)
