The Irish midfielder was close to making the substitutes' bench for the 1-1 draw at Barnsley last Saturday and could soon follow the likes of Tom Cairney, Mark Cullen, Will Atkinson, Liam Cooper and Jamie Devitt into Nigel Perarson's first-team plans.
Hull's assistant manager Craig Shakespeare said: "Gavan has been joining in with the first team of late. Stuart Watkiss and Nick Barmby have both given him a good appraisal from the reserves and he's done really well training with the first team.
"We felt that justified including him (in the squad at Barnsley). It will have been a good experience for him to be part of that and I think what it says to all of the young lads is that if your application is there and we feel that you can have an impact, then we'll include you."