Fallon, 28, has been put up for sale by Plymouth Argyle but is reluctant to drop into League Two.
Moore said: "I think he is waiting to see whether Swansea come in, and that's a shame, but we are keeping an eye on the situation."
The Millers have missed out on another former Barnsley striker Jon Macken, who decided to join Walsall this week instead.
Moore is still interested in signing his son Ian, but has described Tranmere's 100,000 asking price as 'ridiculous.'
Millers chairman Tony Stewart has issued a plea for bigger crowds. Less than 4,000 supporters attended the opener against Lincoln yet 18,000 made the trip to Wembley for the play-off final.
"We want the fans to come and have a look – not just at a play-off final. Their attendance is a key factor in our success."