The Pompey goalkeeper, who had not played a league game since January 2006, has stepped up to play the past two matches for the Blues in the wake of David James' injury.
With James still recovering from the calf strain that has kept him on the sidelines since the defeat at Manchester City, Ashdown looks set to retain his place for the club's final Premier League fixture of the season at home to Fulham on Sunday.
It's been a frustrating period warming the bench for the former Reading keeper behind the continued good form of James.
But he insists he would be tempted away from Fratton Park only if Harry Redknapp was prepared to let him go and the right offer came along.
Ashdown said: 'I'm under contract here, but of course I want to play. I guess it's down to the gaffer if he wants to get rid of me.
'But I'm not going to go banging down his door unless it's a top side who want me to be honest, or a big one in the Championship.'
Although he is not actively looking to end his four-year association with the club, Ashdown knows he may have to find regular first-team football sooner or later.
At 27 years old, he is approaching his peak as a goalkeeper but he admits his laid-back style disguises his ambition.
Ashdown said: 'I may come across as laid back but I'm quite demanding on myself.
'When I'm out there, I'm just as demanding as David James. It may not come across, but it is still there.
'The more you play, the more the hunger comes in.'
Just like Steve Harper at Newcastle, Jason Brown at Blackburn or Tomasz Kuszczak at Manchester United, the life of a number two goalkeeper is frustrating as you wait for the injury or red card that thrusts you into the spotlight.
But Ashdown has not been simply kicking his heels waiting for his chance as he continues his goalkeeping education.
He said: 'Of course I learn from working with Jamo everyday but the way he trains is different to me.
'Everyone is completely different and trains differently.
'That doesn't mean there aren't things I can learn from him – even the small things he does on and off the field. You take a bit here and there.
'But you can learn from everyone. You can even pick up things from some of the young lads at the club.'

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