The Wales international, who currently plays domestic rugby for Toulon, has been linked with Wasps as the club look for a new full-back.
Charles Piutau's spot needs to be filled next season as the Kiwi has agreed to join Ulster.
"Leigh Halfpenny is an obvious one because of the Charles Piutau situation but we have got Rob Miller as well - he is an England Saxon in his own right," The Mirror quotes Young as saying.
"We will make no bones about it - this is recruitment season and we are looking at getting the best for us. I know Leigh really well. I was at Cardiff when he came through the system. We all know he is a quality player. I am just looking forward to seeing who we get linked with next week."
Halfpenny joined Toulon from Cardiff Blues in 2014.