And the Liverpool keeper has revealed he would welcome a loan return to Fratton Park.
The 20-year-old made 13 Pompey appearances before a calf injury ended his season prematurely in April.
Fulton impressed during his time at the Blues – a period which saw him feature in senior football for the first time.
The Burnley-born youngster remains highly-regarded at Anfield, signing a new three-year deal in December.
But he continues to sit behind Simon Mignolet and Danny Ward, while the Reds yesterday added Mainz’s Loris Karius to their ranks.
As a result, Fulton is desperate to embark on another loan spell next term to aid his development.
And he would consider reuniting with Paul Cook’s side.
He told The News: ‘I loved it at Pompey, it’s such a big club which is going in the right direction now.
‘To be honest, with Mignolet and Ward off to the Euros, I think I will be with the Liverpool first team for pre-season. From there I’ll see what Liverpool say and what they want me to do.
‘Obviously, I want to go back out on loan somewhere. It would be great if it was Portsmouth, but I just want to play first-team football so I’ll see what it brings.
‘I want to be a regular and enjoy my time playing football. Liverpool is a great club to be at but it’s a lot different when you start playing first-team football, you realise it is so much bigger and better.
‘Liverpool want me to go out on loan, which is great as it’s a chance for me to try to impress, but at the same time show my worth to Liverpool.
‘I have told Paul Cook I would love to go back. I enjoyed my time, it’s a lovely city, and I’m more than happy to be back down there.
‘Wherever I end up it could happen at the end of pre-season. I am not too sure what is going to happen, whatever comes, comes.
‘I’ve just got to train hard and, if a club comes in, make sure I am fit and ready.’
Fulton had the distinction of saving a penalty on his debut in the 1-0 defeat to Oxford United in January.
He was also in Pompey’s first Football League side to have a keeper net against them – in the form of Morecambe’s Barry Roche.
But he has relished his Fratton Park learning curve.
‘I had a conversation with my family when the chance to go to Pompey first came about,’ added Fulton.
‘I got a little bit nervous but reminded myself this was what I had wanted to do all my life, it was my chance so go and enjoy it. I couldn’t let nerves affect it.
‘It was great for me, I gained so much experience from it.
‘I had a keeper score against me but the downs are stuff to learn from. I gained so much from going there and playing in front of that noisy crowd.’