After bringing in Allen's former Eagles teammate Tom Barrass and ex-St Kilda tall Josh Battle in the off-season, the Hawks would like to add further depth to their forward half.
Allen, who has kicked 139 goals in 93 games for West Coast, becomes a free agent this year and is firmly in the sights of reigning premiers Brisbane as a replacement for their retired spearhead Joe Daniher.
The 25-year-old is understood to have already met with the Lions, with Brisbane having had 12 months to privately grapple with Daniher's looming exit.
Moore, Hawthorn's vice-captain, would welcome any good player who wanted to play for the Hawks, after The West Australian newspaper on Friday reported the club was interested in Allen.
"I think any talent trying to come through the door is great," Moore said at Melbourne Airport on Saturday.
"That's not something that I'm that interested in. I don't work in recruiting either, but hopefully they're doing something in the background."
Former West Coast coach Adam Simpson, who is working in the media this year, on Saturday insisted Allen "wants to stay" with the Eagles.
It has been a stunning turnaround for Hawthorn to become a destination club.
After not winning a game last year until round six, the Hawks surged into early 2025 premiership favouritism, ahead of the Lions, following their impressive 20-point defeat of beaten grand finalists Sydney at the SCG on Friday night.
Moore's appearance at the airport on Saturday was in stark contrast to almost 12 months ago when he was fuming following a poor defeat on the Gold Coast that left Hawthorn 0-5.
The dynamic forward then told his teammates to "bring your mouthguard" to training.
"The mouthguards thing was all a little saga, but it was more just at training," Moore said on Saturday.
"We didn't bring the intensity and we weren't trying hard enough.
"And we know if we don't try hard enough as a football club, we're not going to be able to perform in any type of game.
"The mentality was that training is going to be tougher, then the games hopefully they get easier."