Super-lightweight Taylor became the first British fighter to be crowned undisputed champion in the four-belt era after twice flooring Jose Ramirez in Las Vegas last month.
Having mastered his current division, the 30-year-old is eyeing a step up to welterweight and a potential showdown with WBO champion Crawford.
The Prestonpans fighter feels his remarkable achievements are only just receiving the recognition they deserve and - without being in a hurry to return to the ring - he is far from finished and eager to keep breaking boundaries and confounding his critics.
"I'd like to become a two-weight world champion. I would love to move up to welterweight and challenge for a world title up there and really be touted as one of the greatest fighters to ever do it from these shores," he said.
"I think I can win that fight with Terence Crawford as well. But I'm not really in a rush. The ball's in my court now and I will fight when I'm ready to fight.
"I believe in my own ability. I have been doubted my whole career. It's always, 'he's a good fighter but...', there is always a 'but' at the end of it.
"Give me my props, I'm undisputed world champion, what do you mean 'but'? I've beaten everyone on the way up, I've beaten the best on the way up as well.
"I am getting the recognition now and rightly so. I have been kind of under the radar for most of my career, letting the results do the talking and now the results are shouting out what I've achieved. It's about time."
Taylor joined Oleksandr Usyk, Bernard Hopkins, Jermain Taylor and Crawford in securing a clean sweep of four belts, after only his 18th professional fight.
While his next engagement is likely to be against a mandatory challenger, the southpaw believes he possesses sufficient punching power to move up a category and feels a bout with fellow unbeaten fighter Crawford - with whom he shares a promotional company - would be straightforward to arrange.
His preference would be for the contest to be staged in the surrounds of Edinburgh Castle but, given family and friends were unable to travel to Vegas for the Ramirez clash due to restrictions, would also welcome another trip across the Atlantic.
"It's an easy fight to happen because he's under Top Rank, I'm under Top Rank, so it's all in-house," Taylor said.
"The only discussion would be where it is, that's the only obstacle we have: is it in Scotland or is it in America?
"Personally I would love it in America again but if it comes to Scotland, even better. I would love to re-do what I just did but properly, with the fans and with my family and friends there to celebrate and enjoy it.
"But the castle is an iconic venue. You've seen it all lit up at night when the Edinburgh Military Tattoo is on during the festival and coming out of the esplanade - that's a once-in-a-lifetime event."
Taylor turned professional in 2015 having won gold at the previous year's Commonwealth Games on home turf in Glasgow.
While he recently referred to welterweight as a "sexy" division when speaking about the lucrative fights on offer, he insists financial matters will not dictate his next move.
"If I was money-motivated, I'd have given up boxing a long, long time ago," he said.
"I've always been driven in terms of glory - being world champion, to be touted as the best fighter. I wanted to be world champion, it was never financial motivation.
"Obviously I want to look after my family and things like that but money's never been the goal."
Taylor's euphoria at conquering his classification following a unanimous decision in the Nevada desert on May 22 was swiftly tempered by a rather subdued homecoming.
Returning to Prestonpans in the mood for a party, the 'Tartan Tornado' was forced into a disheartening period of self-isolation because of Covid-19 regulations.
"My mum and my missus came to the airport to see me, so I gave them a big cuddle but I had to jump in the car and go straight home and isolate," he said.
"I never really got to embrace them so it was pretty sh*t that week because it was like, 'I've just done this and I have to sit in the house and stare at four walls'."
"I was on top of Mount Everest and I wanted to have a party and a celebration and I felt like I was in a ditch, in a slump, back down to earth with a bang. I was out doing the gardening. I was kind of fed up.
"I'd just achieved the best thing in my life and wasn't able to celebrate. People wanted to come and see me; my home town was out in Prestonpans but I couldn't get out and embrace it.
"I was just waving in the car and I felt, 'this should have been one of the best and most memorable moments in my life and it's been tarnished by all of this sh*t'."