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:
6:20am Friday 27th March 2015
OXFORD United fans are being encouraged to try something a little different with the launch of a footgolf course.
4:00pm Thursday 26th March 2015
OXFORD United have signed Peterbrough striker Kyle Vassell on loan until the end of the season.
8:00am Thursday 26th March 2015
Sam Long hit the opener and made the second as a youthful Oxford United development side beat their Oxford City counterparts 2-0 yesterday.
8:00am Tuesday 24th March 2015
Midfielder Michael Collins says head coach Michael Appleton’s calm persona will help banish Oxford United’s relegation fears.
9:30am Monday 23rd March 2015
MICHAEL Collins believes Oxford United’s players have to fight for their livelihoods and be willing to put their bodies on the line for the sake of the club’s Football League status, writes JACK JOHNSON.