The 23-year-old twisted his ankle in the 27th minute of the Wallabies' 43-18 win over England in Melbourne at the weekend but scans are likely to reveal he will only miss one match.
"Rodney will have an MRI on his ankle [on Monday afternoon] but he's shown a lot of improvement over the past two days," Connolly said.
"We will rest him from this weekend's match but at this stage we're hopeful that he'll be available for the first Tri-Nations match against New Zealand."
The 130kg prop has impressed in his two matches against England, scoring a try in his debut Test in Sydney, but Connolly felt his front row was not given a good enough workout in the second Test.
"I thought the scrum was good (in Melbourne)," Connolly said.
"I thought we took a reasonable step on both sides and we were a bit disappointed it went to uncontested scrums because these young guys need as much scrummage as they could.
"I didn't think we were under as much pressure (in Melbourne) as we were in Sydney. We would have liked it to be a scrummaging battle."
Al Baxter is the likely replacement for Blake, but Connolly hinted there could be several other changes ahead of his side's one-off Test against the Irish in Perth.
"With Rodney Blake injured we will review the front row - you would think Al Baxter would play," Connolly said.
"We will also review the back row again. We have been very happy with (Rocky) Elsom and George Smith has been wonderful and we will look at that.
"I will be surprised if George (Gregan) doesn't come back and Sam (Cordingley) will be off the bench next week.
"(Winger) Clyde Rathbone is another consideration so we will review a number of things I guess."
Flanker Daniel Heenan remains a doubt with a shoulder injury.