The forward, 25, joined the Cod Army last summer and scored 11 goals in 44 games, finishing with the winner in the final day win against Crewe Alexandra.
His efforts helped secure Fleetwood's status in the third tier, at the expense of Blackpool and Doncaster.
"I'm keen to stay, I'm not shy to say that," Grant told BBC Radio Lancashire.
"I want to be a part of it, if I can, and score more goals next season because I should have scored more this season.
"If I'm part of the journey for however long to come I'll be happy."
Grant's relationship with manager Steven Pressley was described by the Scottish boss as "love-hate".
Pressley publicly criticised the Liverpool-born player for a "disrespectful" attitude to being substituted earlier in the season but he says there is no ongoing issue.
"I know that there's been several things said in the media, but if you ask Bobby he'll tell you we have a great relationship," Pressley said.
"He understands the boundaries, he's an emotional player but I like that."
Grant added: "It's two personalities that are going to clash, two fiery characters that want to win.
"It's two people who want the best for each other and that's what we have.
"As long as we understand we both want to go forward and want to win that will happen."
Striker Bobby Grant wants to stay at Fleetwood Town beyond his current deal, which will expire at the end of next season's League One campaign.