The 28-year-old is one of a handful of players Blades boss Chris Wilder wants to sign a new contract, with the likes of John Lundstram, Enda Stevens and John Fleck already in talks over new deals.
Wilder has said he is "100 per cent certain" that Norwood will reach an agreement with the club – a belief the former Northern Ireland international was happy to confirm.
"It's nice that the club want me to stay here," he said. "I've spoken to the manager and the powers that be. We'll get there. It's as simple as that.
"Why, from a personal point of view, would I want to go anywhere else? It's a special place to be and arguably I want to be here for the rest of my career. I can't see myself leaving and why would I want to?"
Norwood joined the Blades from Brighton, Saturday's opponents in the Premier League at Bramall Lane, at the beginning of last season, helping the club win promotion to the top flight.
He has made 26 Premier League appearances this campaign as Wilder's side have taken the division by storm, putting themselves firmly in contention for a Champions League spot with 12 matches remaining.
Asked if qualifying for that competition, or the Europa League, is now a realistic target for a team written off as relegation favourites at the beginning of the season, Norwood said: "We've put ourselves in a good position.
"It would be silly to say we don't dream or that we haven't spoken about it among ourselves. But we know it's going to be tough and we know there's a long way to go and that we're still not there yet.
"But I do think we've earned everybody's respect. We have put ourselves in a wonderful position but nobody is settling – the manager wouldn't let us settle."
The Blades have returned from their winter break in Dubai with a fully fit squad. David McGoldrick was an unused substitute in the win against Bournemouth on February 9 after a foot injury but the striker has now fully recovered from the problem.