"He does a few things each game where it's like, geez, you really have to be switched on," Meek told AAP of his Brisbane Lions counterpart.
"In our last game, he pushed me under the ball and kicked a good goal at a stoppage.
"You replay those things in your head that many times ... but you learn from them and I'll try to get him back."
Draper took the spoils in a 67-point Lions win last month, and the pair meet again for another crucial ruck battle in Saturday's preliminary final at the MCG.
Darcy Fort will assist Draper but there is doubt over the Hawks' combination, with Ned Reeves pushing to return from a throat injury.
Meek has also enjoyed back-up from key forward Mabior Chol and versatile defender Josh Weddle this season when Reeves has been out of the team.
"I'm pretty sure he should be right ... but I enjoy both (combinations), however the team sees fit," Meek said.
"Brisbane have two good rucks, so we'll see what the coaches are thinking. Whatever happens, I feel like we can embrace what's ahead of us."
Former Essendon big man Draper has shone in his first season with Brisbane, adding his trademark energy to a side gunning for a third straight premiership.
"I actually know him a little bit off-field and he always has a good chat. It's funny with the rucks, we all know that we're good people," Meek said.
"But it's the most combative position on the ground, so you have to wrestle and fight each other for the whole four quarters.
"You just really have to be a able to batten down the hatches when he's in those little periods because he can really turn it on for a five-minute patch and be quite explosive for them."
Hawthorn coach Sam Mitchell has adapted to new interchange rules by often deploying Meek and Reeves in tandem when both have been fit this season, with the pair combining in 15 games.
Meek, who quickly took the No.1 mantle in 2024 after arriving from Fremantle, admits both men found it tricky to adjust to the mental demands of splitting game time and spending extended periods on the bench.
"It took us a little bit of time - even we were speaking about it - to have flow in the game," Meek said.
"But as a team, it helped us so much collectively and once we were able to buy into that it certainly did help.
"He's got the tap work and the ruck craft, and the mids in centre-bounce love him because he can really put it on a platter.
"I'm a bit more of a follow-up and tackle, and grunt work and run. We really complement each other well and the mids love it because they've always got a fresh ruck on the ground."
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