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:
8:00am Tuesday 2nd June 2015
Oxford United’s Callum O’Dowda played for just over 70 minutes as Republic of Ireland Under 21s were beaten 2-1 by England C in Galway yesterday.
8:00am Tuesday 2nd June 2015
Oxford United’s much-criticised Kassam Stadium pitch was laid bare yesterday as preparations began to lay a new semi-synthetic grass.
6:00am Monday 1st June 2015
DIGGERS will rip into the outdated playing surface at the Kassam Stadium today to make way for a completely new pitch.
9:30am Monday 1st June 2015
WHILE the rest of the Oxford United squad have their feet up, Callum O’Dowda has been happily putting in extra training sessions ahead of two games for Republic of Ireland Under 21s this week, writes DAVID PRITCHARD.
9:30am Saturday 30th May 2015
Oxford United’s pre-season preparations have been boosted by the confirmation of a training camp and a match in Austria.