Taylor, 18, captained England at the recent Under-19 World Cup in Bangladesh, where the team finished fifth overall.
The off-spinner, who made his Hampshire debut in August 2013 aged 16, is looking to make a big impact in 2016.
"I'd definitely like to be pushing my way into that team with a few solid performances," said Taylor.
Taylor failed to make a first-class appearance last season and faces competition for a slow bowling place with all-rounder Liam Dawson and leg-spinner Mason Crane.
"With potentially Liam Dawson being away on England duty early season, it might bring up an opportunity, " Taylor told BBC Radio Solent.
"I'm batting well at the minute, if I can put some performances in with the ball too, who knows?"
Taylor took just two wickets in six games in the Under-19 World Cup, but admitted leading his country was "an amazing opportunity".
"It was a bit disappointing to go out in the quarter-finals with the ability and potential we had," he added.
"Going to a country you've never played before, I definitely think it makes you a better player in terms of dealing with pressure.
"I definitely enjoyed the captaincy. It was a brilliant learning curve for me and I took a lot out of it, especially seeing what other captains did, in an environment you're not used to."
Hampshire slow bowler Brad Taylor is targeting more appearances in first-class cricket this summer.