The Wolves loanee, who has not featured for his country due to injury since November 2011, has played in the Glovers' last three matches since being borrowed by boss Gary Johnson.
And, having been recalled to the Wales squad ahead of their qualifiers with Macedonia and Serbia, Hennessey told Press Association Sport that he is hoping first-team football will help him oust Boaz Myhill as his country's number one and add to his 38 caps.
"Of course it is something I am targeting," he said.
"Boaz has gone in and done well, but the only goalkeeper who was playing weekly was Owain Fon-Williams (of Tranmere), the young lad.
"So hopefully me back playing games will ask some questions for (Wales manager) Chris Coleman and we'll see."