After six years at Victoria Park, Liddle thinks it is time to try something new and the possibility of a move to the Championship appeals to the player.
Bristol City, who have successfully stayed in the second tier of English football for a further season, are keen to become play-off hopefuls next time around.
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And the Robins' manager Derek McInnes has been keeping an eye on Liddle in recent months, along with a number of other clubs aware the Teessider's contract was up for renewal.
His former club Middlesbrough have previously considered taking him back to the Riverside Stadium, although a return to his hometown club is looking unlikely.
But there are going to be numerous other options available to Liddle, who will officially become a free agent this summer.
Coventry City, relegated from the Championship, are also in the frame, as are Notts County, Carlisle United and Yeovil Town.
Liddle, though, is in no rush to make a decision and is keen to weigh up all of the clubs available to him before deciding his next move.
The 25-year-old, who joined on a free from Middlesbrough in 2006 after graduating through Boro's academy system, has left Victoria Park on good terms.
Hartlepool manager Neale Cooper, aware of the interest in the versatile middle-man, has indicated he would be happy for Liddle to have a change of heart.
Cooper said: "I really like Gary, he is honestly one of the nicest blokes I've worked with. I understand why he's chosen not to sign the contract.
"I made a similar decision when I was a player with Aberdeen and sometimes you just feel you need a new start. I can relate to him in that sense.
"But the door is always open for Gary and if things don't work out then I would welcome him back here with open arms. I wish him all the best and he certainly leaves with no hard feelings whatsoever."
Liddle made 284 appearances for Hartlepool, scoring 21 goals, and there has been speculation linking him with a move at different stages of the last couple of years.
Last summer Middlesbrough were among a number of clubs keeping an eye on him, only for Hartlepool to exercise the option of a further 12-months on his contract.
Norwich City, prior to their promotion to the Premier League a year ago, had also been admirers.
Hartlepool are aiming to strengthen their squad before the start of the new season in August, with Cooper particularly interested in adding at least one new striker.
Former striker Steve Howard, released by Leicester City this week, is an avenue he is exploring. The 36-year-old, from Durham originally, left Hartlepool in 1999 and has played for Northampton, Luton, Derby and the Foxes since.