The Dubliner revealed how he has been in touch with Renner, who he starred opposite in 2003’s SWAT, after the 52-year-old was left in a “critical but stable condition” after the incident.
Speaking at the National Board of Review Annual Awards Gala in New York on Sunday, 46-year-old Farrell said: “Yeah, I’ve been in touch. He’s doing good, I believe.”
He added: “All prayers are with him.”
Earlier this month, it emerged that the Hawkeye star had been helping a stranded family member in heavy snow when the incident occurred, with the 911 report revealing that he had been “completely crushed” by the snow plough.
The Irish actor also opened up about his new film, The Banshees of Inisherin, directed by Martin McDonagh, in which Farrell starts alongside Barry Keoghan and Brendan Gleeson.
McDonagh’s black comedy sees Farrell play Pádraic Súilleabháin, an Inisherin resident who is struggling to come to terms with the fact his best friend Colm Doherty (Gleeson) no longer wants to be associated with him.
Set in 1923 during the civil war, McDonagh’s flick is hotly tipped to win big throughout this year’s awards season.
“I loved working on this film for probably very obvious reasons,” Farrell said. “The script was extraordinary. I was working with people that I have a lot of love for and that I’ve worked with before and I have a lot of history with.
“And I got to go home, to, you know, my home country, and see parts of the country and shoot in parts of the country that I don’t get to go to very often. It was an extraordinary experience,” he added.
Jeremy has undergone two surgeries for blunt chest trauma and orthopaedic injuries after he was crushed by the 14,330lb snow plough on New Year's Day near his Nevada home.
According to Washoe County Sheriff Darin Balaam, Renner had been clearing snow from a private driveway when his snowcat started to roll away, and he was injured attempting to get back inside the vehicle.
Since his accident, Renner has since shared photos from hospital documenting his long road to recovery.
Some of his other co-stars have rallied around Renner since his accident, with Chris Pratt and Chris Hemsworth all sending their well wishes in recent days.
Aussie actor Hemsworth, who plays Thor in the Marvel Cinematic Universe, wrote: “Speedy recovery buddy. Sending love your way”, while Chris Evans, star of Captain America added: “Tough as nails. Love you buddy.”
Pratt, who plays Peter Quill in the Guardians of the Galaxy franchise, added: “Continued prayers your way brutha”, while British star Paul Bettany, who portrayed Vision in the MCU, wrote: “Love you mate. Sending you love and healing.”
Marvel directors Taika Waititi and the Russo brothers also wished Jeremy well, with the latter writing: “Sending all of our love, brother, and hopes for a speedy recovery.’
“My brother, I love you,” added Taika.
Other famous faces who sent positive messages included US talk show host Jimmy Fallon, actors Vanessa Hudgens and Penelope Cruz, Orlando Bloom and Heidi Klum.