Brunskill – who has scored 87 goals in 166 games – has been at the centre of recent speculation abouthis future on the club's website forum.
But Harry Dunn, who recently returned for his second spell as Blues manager, said: "I spoke to Danny over the weekend, he is looking forward to pre-season, a new regime and new ideas.
"Players like Danny don't come about willy nilly and when you have a good goalscorer, you make sure you keep hold of them.
"He's very upbeat and maybe realises he hasn't done as well as he could have done last season and we will try to make it enjoyable."
Dunn is keeping tabs on former Scarborough FC skipper Denny Ingram.
The defender has yet to complete a switch to a new club since his release from Harrogate Town at the end of the Blue Square North season.
Dunn said: "Denny is a very good quality, experienced player who has been around Conference level for a few years now and knows what it's all about."
Dunn has spoken to two of his former Blyth players, Alex Gildea and Ged Dalton, about a move to the Turnbull while Alex's brother Liam will be joining up with his former Whitby team-mates this summer.
Striker Ant Ormerod has also expressed an interest in a return to the club.
Dunn is confident his side will perform much better in the UniBond top flight next term and avoid a third successive brush with relegation.
"Whitby had the makings of a half decent side last year and for whatever reason, it didn't materialise," he said.
"We will have to get the best out of the players.
"The last thing we want to be doing is fighting relegation – we want to be giving the supporters something to shout about."