METAIRIE, La. -- One of the NFL's most unique players, Taysom Hill, agreed to one of the league's most unique contract extensions Monday with the New Orleans Saints.

Sources told ESPN's Adam Schefter that Hill's new deal will pay him $40 million over the next four years if he remains in his current role in which he serves as backup quarterback, running back, wide receiver and tight end, as well as being a special teams ace. However, the deal can be worth up to $95 million if Hill becomes the Saints' starting quarterback over the next four years.

The deal includes $22.5 million in guarantees. Hill, 31, was scheduled to become a free agent after this season after he signed a two-year, $21 million extension with the Saints in 2020.

The Saints had some salary-cap incentive to get an extension done with Hill before his contract voided next spring. They would have been hit with $8.9 million in dead-money charges against the cap when his contract expired -- and now they can spread those cap charges over future seasons.

But the Saints (5-5) are also showing how much they still value Hill as part of their offense going forward, even though he lost the starting quarterback battle to Jameis Winston this summer and has not yet overtaken current starter Trevor Siemian in the role.

New Orleans will be facing severe salary-cap constraints again next offseason, which will force the team to part ways with some key players for the second straight year -- and could limit how much the team is able to spend on a starting quarterback. Winston is also scheduled to be an unrestricted free agent as he recovers from the torn ACL he suffered in Week 8.

Hill is now guaranteed to be part of the Saints' future in one capacity or another. What remains to be seen is how seriously New Orleans considers him as a starting QB candidate for the rest of this season -- and beyond.

Part of the reason Hill hasn't started any games at quarterback so far this season is because he was dealing with a concussion in Weeks 5-8 and a foot injury this past week that held him out of practice on Wednesday and Thursday. It remains unclear whether the Saints will consider switching from Siemian to Hill at some point to help shake them out of their current three-game losing streak.

Siemian has performed fairly well in the role over the past three and a half games. However, he had his worst struggles to date in Sunday's 40-29 loss to the Philadelphia Eagles, with two interceptions, including a pick-six in the final minute before halftime.

The Saints have a short week to prepare for Thursday night's game against the Buffalo Bills in the Caesars Superdome.

Hill has had a quiet season so far. He is 7-of-8 passing for 56 yards with no touchdowns and one interception. He has run the ball 20 times for 104 yards and three TDs. And he has four catches for 52 yards.

However, the 6-foot-2 221-pounder, who starred as a dual-threat quarterback at BYU, has been a dynamic part of the New Orleans offense since 2018 after the Saints initially claimed him off waivers as an undrafted rookie from the Green Bay Packers in 2017.

Hill went 3-1 as New Orleans' starting quarterback in 2020 while Drew Brees was injured. For his career, he is 101-of-142 passing (71.1%) for 1,103 yards, 4 touchdowns and 4 interceptions. He has run the ball 171 times for 913 yards (5.3 yards per attempt) and 14 touchdowns. And he has 34 catches for 388 yards and seven TDs.

When asked two weeks ago whether he hopes to receive another opportunity at the starting QB job, Hill said, "Of course."

"I think I've been transparent from day one about what the end goal has been here for me. So I don't really know what to say other than you do your best to stay ready," Hill said. "Obviously there's this whole other role that's there for me. So I'm trying to find a balance of staying ready to be able to do that job at a high level, but it's not always the easy thing, because there's this whole other expectation for me that I need to make sure I'm prepared to do. So I'm trying to manage that."