Barrie McKay is in talks over a new deal with Rangers
Warburton now hopes an agreement can be thrashed out to keep the 22-year-old beyond the 18 months remaining on his contract.
While the manager acknowledged Rangers are a selling club, there were no bids for McKay despite rumours of RB Leipzig lining up a £6million swoop.
Warburton said: “I wouldn’t have been shocked if someone had come in because he is a talented player.
“I am sure every club in the Premier League is saying the same thing. When I look at some of the prices being paid for defenders – £7.5m, £8m, £10m, £15m – at what stage do you sit and think, ‘Is there value elsewhere?’.”
Rangers, who visit Hearts on league duty tonight, have opened talks with McKay over an improved deal.
Mark Warburton thinks the deal will be taken care of quickly
Warburton said: “I am sure the discussions will go on between the powers-that-be and the representatives. That should reach a fairly swift conclusion, I’d like to think.
“We just had Barrie in the office saying that he has to work even harder and push again. He can go as far in the game as he wants to.”
Warburton signed keeper Jak Alnwick from Port Vale as a replacement for Wigan-bound Matt Gilks.
He also captured Emerson Hyndman and Jon Toral on loan during the window and there has been criticism of his failure to land players on long-term deals.
While fans want Rangers to compete with Celtic on the field, there is a huge gulf in finances off the park.
Warburton is focused on taking the club back into Europe next season and rebuilding slowly but surely.
He hopes everyone at Gers, directors included, remain realistic in their ambitions when it comes to challenging their Old Firm rivals.
— Rangers FC (@RangersFC) January 31, 2017
Warburton added: “We’re in a different pond to them right now and our job is to get into the same pond.
“It won’t happen right now, it won’t happen by the end of the season.
“Our job is to highlight progress we’ve been making, set targets and achieve them. But the targets have to be realistic.
“It’s a club who have been promoted. Yes, we have a fantastic history, but we are where we are and I hope we can communicate that.
“The worst thing Davie Weir and I can do is set unrealistic targets.
“But getting into Europe is a realistic target.”
Rangers head to Tynecastle two months after they were beaten 2-0 there in Robbie Neilson’s last game in charge of the Jambos.
But with nine new signings in January and injuries to John Souttar and Callum Paterson, Ian Cathro’s side will bear little resemblance to the one which put Rangers to the sword in December.
Warburton said: “My initial glance at their signings is that there’s some good quality but maybe lacking some match fitness. We’ve got guys working to see what we can find out.
“It’s about Rangers performing and dealing with what we have to deal with.”