The Argentine spent two years on loan at Old Trafford from 2007 to 2009, winning the Champions League in the process, before leaving the club to join rivals Manchester City.
Tevez has recently returned to Eastlands after a spell away from the club following a falling out with manager Roberto Mancini, with Ferguson revealing that he was "hesitant" about signing the striker.
"He is a man for a big game Carlos Tevez, there’s no question about that," Ferguson told BBC Radio 5 Live.
"He’s a big game player and he did well in his season with West Ham, and it was an easy solution because he was loaned to us and we paid the loan fee for that two years and then we had the option to buy him.
"But by the time the option came round, we were maybe a bit slow of course, but his agent was everywhere with him. And the money we were quoted was not what he eventually went for, it was a lot, lot more.
"A deal could’ve been done if we’d acted earlier on, but I was just a bit hesitant about it, I wasn’t quite sure."
The 70-year-old also discussed Rio Ferdinand, revealing that he tried to sign the centre-half from West Ham at the age of 17, before eventually securing the defender’s signature from Leeds United in 2002 for £30 million.
"We tried to get him when he was 17, so I feel I’ve been tracking him all his life," Sir Alex continued.
"Their [West Ham] trainer was a guy called Brown at the time, and we phoned him to buy Rio at 17, he said we’ll do a part exchange with Beckham."
Ferguson also noted the prominent role Ferdinand plays at the club, discussing how the England international can be influential amongst younger players, with the defender currently helping out midfielder Paul Pogba, whose future at Old Trafford remains in doubt.
"We tracked Rio for a long time, and he’s matured and become an important figure within the club. He’s good with the players, good with the young players," he added.
"At the moment he’s working hard on the young boy Pogba, he’s not sure what to do. He is well regarded, Rio."
Ferdinand has struggled with injuries over the past few seasons, with his first-team appearances often limited due to recurring problems, and the Scotsman has admitted that the 33-year-old may have lost some of his agility and pace in recent years.
"It’s hard for Rio to have so much speed and agility, then he gets to 33 and he’s lost a bit. Maybe 10-15 per cent of it, so he’s had to change his game. He used to gamble, Rio, when a guy was slipping away from him he’d [sprint back] because he could [go into] overdrive. He can’t do that now.
"I spoke to him about it, I said ‘look, you’re not the same player you were five years ago, you cannot expect to be and you’ve had the back injuries’. You have to take care of that, he does the yoga now which is good. So just adjust your game, step back a yard.
"You don’t need to be there on top of him [a striker] knowing your pace is going to get you out – that’s not always going to get you out. He can maybe read the situation better now – he’s doing great, better than he ever did."
With Ferdinand having already ruled himself out of the running to replace John Terry as England captain, the former Aberdeen boss discussed the advice he gave to the centre-back when he was stripped of the armband last year.
"When the captaincy as taken away from and I spoke to him about it, I said 'look put that out of your mind'. He said 'maybe it’s a good thing, I can concentrate on my job here'. I said 'Rio, it’s the same with us, I can’t have you captain when you’re not available every week'. He took that perfectly well.
"It’s just about coping with an ageing player. Scholes and Giggs do the yoga. Scholes has come back nice and fresh," Ferguson concluded.