Rhinos have a vacancy after Ryan Hall joined Sydney Roosters at the end of last season.
His squad number five has been handed to academy graduate Ash Handley, but Briscoe – who will wear No 24 – is determined to stake his own claim over the final two months of pre-season.
“There’s a couple of outside-backs so we will be fighting it out for that position,” predicted the 24-year-old prolific try scorer.
“That’s what they told me towards the back end of last season – there’ll be that spot available.
“There’s me and Ash [Handley] and Ashton [Golding], so there’s a few players battling it out for it.
“That’s what he [coach Dave Furner] has told us, whoever trains best in pre-season, that’s the shirt there for you. That’s what we are all going for.”
Briscoe rejoined Rhinos, for his third spell at the club, in June after impressing for his hometown side Featherstone Rovers.
He touched down five times in 10 games and has now signed a long-term deal.
“That’s what I was playing for last season, a good contract,” he said.
“Getting three years now I have just got to keep building on top of that and go from there.
“For me personally, I thought I had a good run [with Rhinos] last year.
“Obviously, some of the results didn’t go our way, but I thought I carried on a good year.”
Briscoe was a try scorer in 17 successive games for Rovers last season, equalling the European record and earning him a nomination for the Betfred Championship’s player of the year award.
His try-scoring feats made him one of the most in-demand players outside Super League, but Briscoe believes he is still far from the finished article.
“I want to kick on,” he added. “I had a decent year last year, but I want to build and get better from that. Hopefully, I’ll get better and better.”
Rhinos have just completed their third week of pre-season training and Briscoe feels full-time preparation will take his game to another level.
“We are more or less all in now apart from the England boys and the new signings,” he said.
“We will have a long time together in pre-season and build on that.
“We’ve got to learn how each other plays and play on the back of that. It might be a different playing style and we’ve got to learn from each other and carry on from there.”
Briscoe is enjoying a new way of doing things under new head coach Furner.
“He has been good,” he observed of the new coach.
“He has changed a few things and it feels like we are on the up.
“Hopefully, we can kick on through pre-season and start the season on a high.”