Downing was targeted by both Sunderland and Newcastle once it became clear he could leave West Ham, but the 31-year-old eventually rejoined Middlesbrough instead.
Downing played for McClaren during his last spell at the Riverside Stadium and holds his former boss in high regard but says the Magpies left it too late for him to consider snubbing Middlesbrough.
“The only thing I heard about Newcastle was from Slaven (Bilic),” Downing said in the Daily Star. “I didn’t get any contact and I didn’t know anything about it until he told me – and that was the day before I came here.
“It was news to me but I was too far down the line with Middlesbrough.
“Once they came in, I spoke to the chairman, Steve Gibson, and he said he could do the deal, so I wasn’t going to say ‘no’.”
McClaren has been handed a hefty transfer budget at Newcastle – the £7.5million signing of Chancel Mbemba will take his spending to around the £35million mark following the captures of Georginio Wijnaldum and Alexsander Mitrovic – but Downing believes that will only make things tougher for the former England manager if the team suffers a poor start to the season.
“I think it will be tough for him,” Downing said. “They’re a very demanding club and crowd.
“He’s spent big on a couple of players and the pressure will be on him to do well.
“I had a really good time with Steve. He’s a very good manager and a good coach.
“He will make Newcastle hard to beat and do the best he can.
“But the Premier League is a very tough league.
“If he does not get a good start, the pressure could be on him, but I hope he does well because he’s a decent man.”
Downing also revealed his disappointment that West Ham dispensed of Sam Allardyce, who he believes he had a future under at Upton Park.
“I was sad to see Sam go – he was great for me and a good man to play for,” Downing added.
“And I got on really well with him. I think I was a big part of his plans.
“But once he left, I had two years on my contract and there were a lot of changes going on there.
“It was always in the back of my mind to come back here.
“I spoke to Slaven about it. I have nothing against him – but he wanted to bring his own players in.
“He did say he was counting on me big time, but when I spoke to him one-on-one, I didn’t get the feeling I got from Sam and from Aitor Karanka when I signed here.”