Cole flourished as a player under Mourinho when the pair were at Chelsea with the Portuguese leading the Blues to unprecedented success.
However, the English midfielder claims Mourinho has his biggest test ahead of him this season which will be to deny Barcelona a fourth straight La Liga crown.
Madrid lead the La Liga table by three points from their bitter rivals Barca but the Catalans still appear to hold a psychological edge in games between the two - Barca recently beat Madrid 3-1 at the Bernabeu earlier in the month.
"If he goes and wins the league, that is the biggest achievement from any manager at any time because that Barcelona team is something else," Cole told talkSPORT.
Cole won two Premier League titles and several Cups with Mourinho before the coach left Stamford Bridge after three years in charge in 2007. In Cole's opinion, there's no question the club made a massive mistake in letting the 'Special One' leave as he has gone on to have success at Inter Milan and now stands on the cusp of winning more trophies with current employer Real Madrid.
"Of course [Chelsea] should have carried on [with Mourinho]. It's plainly obvious he should still be there," he said.
"He was a big, big influence on my career. I remember the first meeting, he got the lads together and said ‘listen guys, you haven't won anything, you have done nothing in the game, if you stick with me we are going to win this league by April'. All the lads were like ‘who is this geezer'? Then we went out to train and the training was blinding, tackles flying in and it was so intense.
"He was just great to play for; you knew where you stood. Looking back I played my best football under him. I won my most trophies under him. He used to get on my back so much but I can't thank him enough for it.
"He saw something in me that maybe I didn't see in myself. If someone tells me I can't do something, I want to show them I can do it. That's why he's a great manager and he's a good guy as well. He'd long gone before I realised that he'd made such an impact on my football. I appreciate everything he did for me."
Cole left Chelsea in 2010 for Liverpool but is now plying his trade on loan at French Ligue 1 side Lille.