The 35-year-old was reinstated as the No.1 wicketkeeper and appointed vice-captain for this Ashes series, but has no plans to stand aside now the campaign is coming to a close.
Haddin currently sits on 25 catches from four Tests. He needs just three dismissals at The Oval to join Marsh and four to break his record, which has stood since the 1982-83 Ashes.
The NSW gloveman was unaware of the pending milestone, praising the consistency of the bowlers for getting him close.
Haddin also made it clear the back-to-back Ashes series wouldn't be his swan song and says he hopes to play on until he's at least 37.
Marsh retired from Test cricket at 36 and Ian Healy and Adam Gilchrist at 35.
If Haddin is still playing Test cricket in two years he'll be Australia's oldest keeper since Hammy Love made his one-off appearance in 1933.
"I think I've still got a lot of cricket left in me now and to the 2015 World Cup. So I'm keen to play there," he said.
"I wasn't aware of that (record) at all. I'd take that back for a win.
"You don't play for them. When they come along it's a nice achievement but I'd take a few wins over that.
"When you tick those milestones off on the way it's obviously flattering but it's also pretty hollow if you don't win any cricket games. From that point of view I'd love to win this one moving forward to Australia."
Haddin had a poor keeping performance at Lord's, with a missed chance of Joe Root in the second innings when the England batsman was on 8, costing Australia dearly.
Root went on to make 180 after England lost three quick wickets for 30 runs.
In contrast Haddin had a stunning match at Old Trafford, where he smashed 65 not out and took a spectacular catch off Peter Siddle.
He's justified his elevation over Matthew Wade, but in the end he has averaged just 25 and Australia must make a decision at some point about whether they need to stick with Haddin's experience or back a younger option like Wade or Tim Paine.
Haddin said he's happy with his form.
"You've still got to perform, you've still got to challenge yourself to get better," he said.
"My batting feels in a good place.
"I feel comfortable with where my keeping is at, it's felt especially good the last couple of games. It wasn't where I wanted it to be after Lord's."