The 29-year-old ended a six-year spell with the U’s when joining Conference Premier side Eastleigh this week.
The striker leaves United frustratingly one-goal short of equalling the club’s all-time record of 107 goals, held by Graham Atkinson.
The landmark is all the more frustrating for Constable, whose hat-trick against Chester on August 18, 2009 is not officially counted because United’s opponents folded later that season.
But while he would have loved to have departed with the record under his belt, Constable says he has not totally accepted he will never break it.
“Never say never,” he said.
“If in a few years’ or so there is the chance to come back to Oxford, of course I would consider it if it’s the right move for me.
“I’d love to return and break the record, of course I would.
“My heart was saying that I should stay at Oxford and try to break it now, but my head was saying that I need the security for my family and that is why I came to the decision that I did.”
Constable admits he has been overwhelmed by the messages of support from United’s fans, and is hoping the club can bring them success.
The striker also revealed he turned down offers from Football League clubs in order to join Eastleigh, with a two-year deal being the clinching factor.
“I’ve seen people saying it was about money, but I could have earned a lot more by staying in the League,” he said.
“I know some will say I shouldn’t drop into the Conference again, but I am excited by the plans Eastleigh have.
“It’s very similar to when I joined Oxford from Shrewsbury – they are a club who have big hopes and I am excited to be part of it.
“I had calls from a League One club and a couple of League Two sides, but the challenge at Eastleigh really excited me.”
Meanwhile, Sean Rigg, released by Oxford at the end of last season, has signed for Sky Bet League Two rivals AFC Wimbledon.
Rigg made 85 appearances for Oxford, scoring nine goals in his two years at the Kassam Stadium.
Latest United news:
2:00pm Friday 19th December 2014
BRIAN Howard’s situation at Oxford United is unclear after head coach Michael Appleton admitted he did not know whether the midfielder would be offered an extension to his short-term contract.
12:00pm Friday 19th December 2014
JOSH Ashby is good enough to play in Oxford United’s side right now, but the teenager knows his time will come, according to head coach Michael Appleton.
9:40am Friday 19th December 2014
RONNIE Moore is braced for a tough first game in charge of Hartlepool United after comparing opponents Oxford United to Real Madrid.
9:30am Friday 19th December 2014
John Campbell admits it would be difficult to keep his kit on if he was able to make an impact on debut for Oxford United tomorrow.
Interactive match preview: Appleton and Hylton on goals; Moore likens United to Real Madrid; Howard's future; Ashby; club stalwart departs + video
9:34am Friday 19th December 2014
Get ready for kick-off with our interactive preview of Oxford United's trip to Hartlepool