The Turtles were narrowly pipped last season as they finished second in the league, three points behind Kelantan, and also lost out to Negri Sembilan in the final of the Malaysia Cup.
However, they did emerge victorious in the FA Cup, beating Kelantan 2-1 in the final, and Mat Zan has warned the Red Warriors his side are ready to give them more problems this year.
"We were beaten to the title by Kelantan last season and the desire to win it for the first time is driving my team forward," Mat Zan told Channel NewsAsia.
"Kelantan are still the team to beat in the Malaysia Super League but we are fighting them every inch of the way."
After booking their spot in the FA Cup semi-finals on Tuesday with a 1-0 aggregate win over LIONSXII, Terengganu continue their league campaign on Saturday when the entertain Johor FC.
Terengganu's city rivals T-Team will also be looking to boost their title prospects this weekend, something which seemed unlikely at the start of the season, when they visit the LIONSXII at the Jalan Besar Stadium.
Like their hosts on Saturday, fourth-placed T-Team bowed out of the FA Cup in midweek when they were beaten by Kedah 2-1 on aggregate, and coach Yunus Alif has demanded improvement from his side when they play in Singapore.
"Last night's [Tuesday's] match was not the game I wanted," Yunus told Bernama.
"It's a lesson the team had better learn in our upcoming matches."
League leaders Kelantan should have an easy match against struggling Felda United on Saturday, while Sarawak can overtake tenth-placed PKNS FC by beating them at the weekend. Sabah face a tough test against Selangor.
On Friday, Negri Sembilan moved to fifth in the Malaysia Super League with a 2-1 win away at Kuala Lumpur.
Afiq Azmi opened the scoring for Kuala Lumpur, before goals Shakir Ali and Shahurain Abu Samah sealed the win for Negri.
Elsewhere Ghanaian Mohamded Hamidan scored twice as Kedah beat Perak 3-0 at the Darulaman Stadium in Alor Setar.
Hamidan's efforts sandwiched a Syazwan Roslan own goal as Kedah ran out easy winners.
Friday's Malaysia Super League Results
Kuala Lumpur 1-2 Negri Sembilan
Kedah 3-0 Perak
Saturday's Malaysia Super League Fixtures
LIONSXII vs T-Team
Sabah vs Selangor
Terengganu vs Johor FC
PKNS FC vs Sarawak
Kelantan vs Felda United