Parker was part of the squad that lifted the Premier League trophy under Jose Mourinho in 2004-05, but only featured for 125 minutes during four appearances and injury prevented him from playing in the Carling Cup final victory over Liverpool that same season.
His limited contribution render his winners medals meaningless in his mind, admitting he does not even know where they are.
But, as Parker prepares to help Spurs overcome Basle in the Europa League quarter-final tonight, he promises a winners medal in that competition will take pride of place in his front room.
“It would have to go on the fireplace,” he said. “That would go somewhere a little more special.
“I’m sure I would treasure it a little bit more than the league one that I don’t even know where it is.
“The manager told us from the outset that we would try to win the competition and it was a big part of our season. If you come away at the end of the season and have won this competition you’ve done very well.
“Every one of us in the changing room wants to be successful and try and win something.”
Spurs will be without striker Jermain Defoe tonight, who is set to miss three games with a pelvic injury, but goalkeeper Hugo Lloris is fit again after knee trouble.