Abraham, who suffered a concussion in Week 1 against the San Diego Chargers on Monday Night Football, left the team last Tuesday. He saw a neurologist Monday, which is one of the last stages of the NFL's concussion protocol, Arians said.
If Abraham is cleared to play, the NFL's active sack leader could be back in the starting lineup Sunday against the San Francisco 49ers at University of Phoenix Stadium.
Arians said Abraham, who suffered his first reported concussion, had been texting him for the last three days. About 30 minutes before Arians met with the media Monday afternoon, Abraham told his coach he could announce his return.
Arians said Abraham talked about a possible return with a couple teammates Saturday night.
"He's ready to play," Arians said.
Abraham entered the season No. 9 on the all-time sacks list with 133.5, eight behind friend Michael Strahan, who sits fifth. Abraham did not record a sack in the season opener and missed Sunday's victory against the Giants.
When Abraham took his leave of absence last week, he told Arians his desire to play had waned. Reports also surfaced that said Abraham had been suffering from memory loss for more than a year.
"A lot of it was to do with the headaches," Arians said. "First real big one he's ever had. There's other things that we're dealing with, and he's fine with those."