The 31-year-old wideout is set to be a free agent after the season, but hopes to finish out his career in Indy.
"I want to be here," Hilton said, via the Indy Star. "But (an extension) takes two sides. That's up to Mr. (Jim) Irsay and Chris (Ballard) to get the job done. For me, I want to be a Colt."
Hilton started the season slowly, but has caught fire in recent weeks. In the last five games, the speedy wideout has generated 408 receiving yards on 24 catches with four touchdowns.
The chemistry between Hilton and Rivers has clicked down the stretch, as the Colts have a chance to earn a playoff spot with a win Sunday over Jacksonville and a loss from one of the teams ahead of them in the standings.
While Rivers pondered recently that Sunday could be his final game, and also perhaps his last with Indy, Hilton did nothing to suggest he plans to walk away.
"No, not at all," Hilton said. "Go out there and play my game, and whatever happens, happens."
In his ninth NFL season, Hilton doesn't plan on wearing anything but a horseshoe for his career.
"Whatever I sign for on my next contract, that'll be when I hang it up," he said. "Whether it's two years, three years, four years, whatever it is. Whatever I sign for on my next contract, that'll be it."
Hilton hopes the Colts also bring back Rivers for at least one more year, so they can continue to build on this season.
"Absolutely, to me, he's come in and done a tremendous job and got us in a great position, so it would be dumb for him not to be here," Hilton said.
The futures of Hilton and Rivers are two big decisions general manager Chris Ballard will have to make this offseason. First, the club will find out Sunday if this season will continue further into January or come to a crushing end.