The prolific striker is poised to put pen to paper on the deal which will tie him to the Dolphins until the summer of 2014.
Byerley signed non-contract terms with Dorchester Town in November before joining Poole on dual registration to boost his match fitness.
But after netting eight goals in 11 appearances, Byerley has opted to commit himself to Poole.
The 27-year-old has settled in well with Killick’s squad following a brief and ill-fated spell as a full professional with Kettering.
And the Dolphins manager was delighted to strike a deal with the former Hamworthy United frontman.
Killick told the Daily Echo: “It helps when you have got a player who is happy and expressing a desire to stay.
“I think he always wanted to stay and it was just a question of coming to an agreement on the finances.
“Until everything is signed, we are not counting our chickens but, so far, the whole process has been positive and relatively quick. Discussions have been very positive and quick.”
Poole’s attacking resources will look increasingly healthy if Byerley completes his paperwork, with Michael Charles already on the club’s books and Dan Cann also in line to sign a new contract as he closes in on full fitness following knee surgery.
Killick added: “If we can get it done, it would mean that we would have Warren and Michael Charles contracted until the end of next season.
“That would be a big positive for us because, in a way, that was our deficiency at the start of this season. We lost the forwards we had at the end of last season and struggled to replace them. Certainly in the early part of this season, without being harsh to the people we had, we were probably not as strong as we wanted to be.
“The other thing is we have still got Dan Cann, who is contracted until the end of the season and has agreed, in principle, something until the end of next season. If we get that done, we would have three exceptionally good forwards in our squad, whether we are in this league or the league above.”
Poole are widely regarded as title favourites in Division One South & West of the Southern League after missing out in the play-offs last season. Their clash at Clevedon Town last night was postponed.