Keane missed out on that honour as he was banned for Manchester United's 1999 final victory, also over Bayern Munich, and he believes Terry's suspension should not cost the Chelsea skipper the chance.
UEFA have confirmed that Terry is permitted to lift the trophy if Chelsea win even though he is suspended.
Keane, speaking at ITV Sport's Euro 2012 launch this week, said: "I think it's only right if Chelsea win that John Terry gets up straight away and lifts it for the first time. He's captain of the club and deserves it."
Keane said United never even asked whether he would be involved in the trophy handover - it was not until 30 minutes later that he and Paul Scholes got their hands on the cup.
The former Republic of Ireland midfielder added: "We lifted it half an hour later and it was nice but I don't think United did anything at all [to ask].
"I don't think it crossed our minds at all. The priority was for the team to win and the bonus is always lifting the trophy so I thought don't worry too much about it.
"But I wouldn't begrudge John Terry the chance if they win on Saturday to pick the trophy up."
Keane empathised with the seven players, four from Chelsea and three from Bayern, who are suspended for the final - all bar Terry for picking up too many yellow cards.
Terry is banned after being sent off in the semi-final for kneeing Barcelona's Alexis Sanchez.
"Yes of course I do," he said when asked if he felt sorry for those suspended.
"You want to play in all the big games. But, what I enjoyed about the semi-finals was the mentality of all the players.
"They were so desperate to get their team to the final that they sacrificed themselves. There have been stories about players on yellow cards in semi-finals missing the second leg.
"These players put the team first. They made sacrifices."