Murray, preparing for his fourth final at Melbourne Park, has twice been denied by upcoming opponent Novak Djokovic in Australia, and the Serb stands in his way again on Sunday.
After the 2015 decider, Djokovic and Murray will have met in a major final as many times as Pete Sampras and Andre Agassi did - five - while they still trail contemporaries Roger Federer and Rafael Nadal, who have played off eight times in grand slam deciders.
Murray said his personal achievements are still worthy of praise, given they have come in an era dominated by Djokovic (seven major titles), Federer (17) and Nadal (14).
If he can win in Australia, he would have ticked off the same boxes as 14-time major winner Sampras, who failed to win at Roland Garros.
"I think obviously it would be a good achievement," a typically understated Murray said, of winning three of the four majors.
"I know winning any of the slams is a very challenging and tough thing to do.
"Like I said the other day, winning three of four slams like in this era seems like nothing because of everything that the other guys have done.
"But it's a very difficult thing to do.
"So whether I win tomorrow or not, I still feel like my record here has been a good one."
Murray said he actively did not watch Friday's semi-final between Djokovic and Stan Wawrinka, but monitored the scores on his phone.
"I didn't watch any of the match last night," Murray said.
"I'll watch some of it this evening and then chat to Amelie [Mauresmo] about it tomorrow. But I haven't watched any of it yet.
He later added: "I'm going to watch the parts of the match that I want to watch this [Saturday] evening, get all of the stats from the match that I think will be beneficial and go over it, just like I have done every other match since I have been here this event.
"But I didn't really want to sit for three, three and a half hours last night worrying about the match.
"I'd rather save that for this evening and try and conserve a little bit of energy and mental energy."