The centre-back went off in the Champions League defeat by Liverpool at Ibrox last week with a thigh injury and initially there was no firm date on his return.
However, ahead of the home cinch Premiership game against Livingston on Saturday, the Gers boss was hopeful of a return at the start of the year following an encouraging prognosis.
He said: “It was a little more positive than we thought.
“The World Cup is five weeks (break) and we don’t have any games so he and the other (injured) players will benefit in their recoveries.
“So hopefully we will have Connor back at that time.”
Midfielder Ryan Jack and centre-backs Filip Helander and John Souttar are out long-term as is midfielder Ianis Hagi, with attacker Tom Lawrence also sidelined.
In an injury update, the Dutchman revealed Glen Kamara will again miss out against the Lions with an ankle knock but should be back for the Champions League game against Napoli in Italy next week, while a scan on fellow midfielder John Lundstram’s ankle injury revealed good news.
He said: “Glen had a problem with his ankle so he has not been in the squad for 10 days.
“He went to London this week and is now back available to train so hopefully we will have him back for the game against Napoli.
“We are a little bit short of midfielders so hopefully Glen will be back for the next (European game).
“We had a lot of scans (on Lundstram) but it was okay. John is fit and has been playing all the games so I am happy.”
The only fresh doubt for the game against Livingston is left-back Ridvan Yilmaz after picking up a knee injury in the Premier Sports Cup quarter-final win over Dundee at Ibrox on Wednesday night.
Van Bronckhorst said: “He got a knock on his knee. We assessed him today to see if he is available but he is the only doubt for tomorrow.
“It will be short-term. He played his first 90 minutes. We have to be careful with him.”