The Coatbridge boxer, who has won titles in three weight divisions, suffered a seventh-career defeat in a unanimous points loss to Crolla in Manchester on Saturday but insists he has no intention of retiring at the age of 34.
Both fighters entered the ring with the hope that victory would enhance their aspirations of again becoming a world title contender.
But promoter Eddie Hearn reckons former WBA lightweight champion Crolla could opt for a lucrative pay day north of the border rather than chase a belt and Burns would love to do battle with the Englishman at the SSE Hydro.
Burns said: “One hundred per cent I would fancy another fight in Glasgow.
“When this fight was talked about we agreed to everything that they wanted, Manchester, even moving back down to lightweight – so I think it would only be fair.
“Let’s get it back at the Hydro. My next fight is going to my 50th and I keep saying to [trainer] Tony [Sims] that I think I can hit 60 or 70. We’ll see what happens.
“My attitude towards boxing has not changed since my first amateur fight.
“Although I lost I still love it; the training, the fighting, everything.
“I’ve been sparring against top-class fighters, all the youngsters, and if I was taking too many punches or not keeping up with them I would know myself it was not for me anymore but that’s not the case and I’ve definitely got a few big fights left in me.
“Staying at lightweight, I think I showed that as long as I diet properly that it’s my best weight to fight at. If they’re up for it then let’s do it. Anthony, let’s get this on again.”
The judges scored the fight 116-113, 117-112, 116-114 in Crolla’s favour but Burns thought he had boxed well.
He added: “It was a good fight and it was a hard fight and I thought I did enough.
“I wasn’t really taking that many clean shots and I was boxing well behind my jab and catching him regularly through the rounds.
“Although he was throwing more punches, I thought he was landing them on the gloves.”
Manchester-born Crolla admits that he is tempted by the prospect of a return bout against Burns in Scotland.
He added: “Why not? I don’t have a problem with that, we’ll go away and assess things but first of all I’m going to have a little break with the family.
“I think we’re very alike and we get amazing support.
“I’m very proud of where I’m from but when Flower of Scotland plays up there at that Hydro I find it hard not to sing along to it.
“I’ve go problem in going there, if that’s the best offer on the table then so be it.
“We’ll weigh up the options and see what’s the best option, my aim is to win another world title and what route gets me there the fastest – I’m likely to take it.”
Promoter Hearn said: “Anthony’s at the stage in his career where world titles are very important but so are the big fights and the numbers, they have not got ten fights left.
“They’re in the final stages of their careers and it’s our job to make sure they get what they deserve, which is as much money as possible.
“That’s what it will come down to. If they both like the money in the rematch then it happens everyday of the week.”