Moore has enquired about defenders, midfielders and strikers as he looks to improve his Rovers squad.
But the 60-year-old expects to have to wait a few weeks yet before he is able to bring some of his targets to Prenton Park.
He told the club's official website: "We've spoken to quite a few players already.
"We've talked to a couple of centre-backs who played regularly in the Championship last season, we've spoken to left-backs, central midfielders and strikers.
"But it's a waiting game at the moment. It's still early in the summer and a lot of players and agents are on holiday and keeping their options open.
"I expect we'll have a few players on trial throughout pre-season and we've approached managers of other clubs about long term loans as well."
Press Association Sport understands ex-Barnsley defender Stephen Foster has agreed a two-year deal with Rovers, while ex-Sheffield Wednesday defender Julian Bennett and Rotherham striker Kayode Odejayi are other reported targets.
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