Jones’ award caps off a stellar season that has seen him lead his country to a Grand Slam and a World Cup semi-final while also becoming Wales’ most capped international of all time.
The 34-year-old lock has been a key figure in each of the last three Lions Tours, stretching back to 2009 in South Africa.
He has featured in the last nine Tests in a row for the tourists, and has not given up adding a fourth and final trip to the home of the world champions in 18 months’ time.
“I am not going to lie, I am aware it’s there, but it’s a two-pronged answer,” said Jones.
“You are never going to say never but you don’t want to be too greedy as well.
“I am fully aware you have to be fit playing well to be selected.
“If the planets align and I am potentially still there, then it’s somebody else’s decision.”
Just last week, Warren Gatland and the Lions unveiled the 2021 tour itinerary with three Tests against the Springboks.
And Jones is certainly in contention to make the touring party, even though the lock has not featured for club or country since their bronze play-off defeat to the All Blacks in Yokohama.
Jones admits the pain of the World Cup semi-final loss to South Africa will push him to new heights.
“The losses still hurt but they inspire you to go on as well,” he added.
“It does spur you on and want to make you go again. We are carrying a bit of hurt from the World Cup.
“I am on a personal level because we went out there believing we could win it and we did not manage that.
“It’s (semi-final defeat) not what I or anyone else wanted.
“We came so close and the margins are so small in elite sport which seem to get closer and closer. You can use that disappointment to fuel whatever the next phase is.
“Having had the Sunday morning after Grand Slams and Championships and winning trophies you still want that.”
In addition to Jones’ individual award, he and his teammates won team of the year while Gatland was also crowned coach of the year.