Gateshead-born Harrison has been linked with Hartlepool United, who parted company with Dave Jones after dropping into the League Two relegation zone.
Harrison says he is flattered but insists his focus is on Sunday's Welsh Cup final against Bala Town.
"I've said from day one that I'm a very ambitious person," Harrison said.
"I want to manage at the very best level I can.
"It's nice to be linked to these jobs. But at this point in time the Welsh Cup Final is the be all and end all for me.
"Once that's finished we'll be preparing for the Champions League and then whatever will be will be."
Saints have already secured the Welsh Premier League title and the Nathaniel MG League Cup, Saints and earlier this season broke Ajax's 44-year world record for the most consecutive wins with 27 straight victories.
Harrison's side will achieve a third successive Welsh treble if they beat Bala in Sunday's Welsh Cup final in Bangor.
New Saints boss Craig Harrison has said he has ambitions to manage at "the highest level."