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:
6:40am Wednesday 1st October 2014
JAMES Roberts admitted it was extra sweet to score a winner for Oxford United against rivals Swindon Town, even if it came in a behind-closed-doors game.
3:26pm Tuesday 30th September 2014
JAMES Roberts came off the bench to score the winner as Oxford United came from two goals down to win 3-2 against Swindon Town at Roman Way.
9:00am Tuesday 30th September 2014
Oxford United’s position in the table is now a concern for head coach Michael Appleton, who has acknow-ledged it is taking longer than expected to improve results.
8:00am Tuesday 30th September 2014
A lacklustre Oxford United Women suffered a 5-0 thrashing at local rivals Reading, writes MATTHEW BRUCE.
10:30am Monday 29th September 2014
MICHAEL Appleton admitted Oxford United were second best where it really mattered as they lost 2-0 at Luton Town.