Houghton is out of contract with the Premier League title chasers in the summer while Rovers are currently looking to extend his loan spell until the end of the campaign.
The 21-year-old holding midfielder has made a major impression since arriving at the Keepmoat at the start of the season and his permanent acquisition would prove immensely popular.
“I’d be open to many options but this would definitely be one,” Houghton said.
“I’ve really enjoyed my time here. I think the main thing is finding a manager that trusts you and I think that is what the manager does here, he trusts me.
“In the long run it would definitely be an option if things don’t work out at Chelsea, it would be an option to stay here.”
For now, Houghton’s immediate off-field concern is discovering his fate at Chelsea.
But once his future is clear, the former England youth international is keen to remain on loan with Rovers beyond January.
“It’s definitely something I want to do,” he said
“I’m still waiting to find out regarding my contract with Chelsea. I’m up at the end of the season so I’m seeing what is going to happen with that end of things.
“Hopefully when that gets sorted we can look to extend the loan because I think at the moment it’s what all parties want.
“I’m playing and doing well which is what all parties want so hopefully it can get arranged that I’ll stay until the end of the season.”
Houghton admits he was attracted to Rovers by the clear goal of winning promotion back to League One at the first time of asking.
He said: “The aspirations for the club were to get promoted straight away, no questions about it.
“This is too big a club to be in League Two.
“I knew we’d be up there from just looking at the players and speaking to the manager.”