Gerrard, a two-time FA Cup-winner, scored twice to give Liverpool a 2-1 win over their valiant fourth-tier opponents on Monday and set up a home game with Championship side Bolton Wanderers in round four.
It was Gerrard's first appearance since he announced that he will leave Liverpool at the end of the season and with his 35th birthday falling on the day of the final, Rodgers is hoping to give him a glittering farewell.
"Well the FA Cup final is on his birthday, so there would be no better way for us to mark it. That would be a wonderful send-off for him," said Rodgers.
"OK, he might be getting a bit older, but he'll always have that world-class ability and world-class talent.
"There are a lot of games to play in between, but we've targeted a cup victory this season, so we're still very much in line for that moving into the second part of the season.
"The team's still very focused and we played some really good football tonight (Monday) on a really good pitch. So the idea is to get a cup run, and if we can do it, that would be really special of course."
The match at the 4,850-capacity Kingsmeadow stadium in south-west London recalled the 1988 final, when the original Wimbledon – dubbed the 'Crazy Gang' – stunned league champions Liverpool with a 1-0 victory.
Gerrard gave Liverpool a 12th-minute lead with a header and claimed the winner with a second-half free-kick after Wimbledon striker Adebayo Akinfenwa, who is a Liverpool fan, had stabbed in an equaliser in the 36th minute.
Wimbledon's committed performance belied the 72 places between the teams in the English league system and beaten manager Neil Ardley felt that Gerrard's class had been all that had separated the teams.
"We got outdone by a world-class player in the end," said Ardley.
"The headline was written for him after the week he's just had.
"I didn't want to be part of anything that positive for him. Our players have still done us proud, but there's that element of disappointment in me at the moment.
"I'm sure there will be a very emotional last game for him at Anfield in the future, but he deserves it. It's very rare to have a player who spends that amount of time at one club."
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