The 37-year-old Palmer hasn't committed to being the Cardinals' quarterback in 2017 for a 15th NFL season.
"I think he'll announce he's coming back real soon," Arians told ESPN on Friday. "I think it's just a matter of letting all the bumps and bruises heal, have a great time with the kids snow skiing ... and he'll be back."
Palmer threw for 4,233 yards with 26 touchdowns and 14 interceptions in 2016, a season in which he missed one game due to a concussion and also dealt with lingering hamstring soreness. He is scheduled to earn $17.5 million next season, which would be his fifth with the Cardinals.
On Wednesday, Palmer addressed rumors about his future with the Cardinals and denied a report that his Arizona home is for sale.
"No, my house in Arizona is not on the market," Palmer said in the statement. "And every year we have taken off for offseason family adventures so there's nothing to read into there either."
The Cardinals found out Wednesday that veteran wide receiver Larry Fitzgerald would be returning to the team for a 14th season. The 33-year-old previously hinted that retirement was a possibility.