Wasps are one of a number of teams interested in Halfpenny, who has been strongly linked with a move away from current side Toulon at the end of the 2015-16 season.
With home-based players being favoured for international selection under Wales boss Warren Gatland, Halfpenny is understood to be keen on a move back to Britain, although Young admits that the 27-year-old will have a number of options.
"We would obviously love to have [him]. We're probably one of six or seven options Leigh's got," Young told BBC Coventry and Warwickshire.
"I couldn't say what Leigh's going to do, but I know he's looking to make a decision over the next two weeks and we're one of the clubs that's an option."
Halfpenny, who has also been linked with the likes of Cardiff Blues and Scarlets, is currently recovering from the knee injury that forced him to miss this year's Rugby World Cup.