Matic, who signed for the Blues for a second time in the January transfer window, trained with Boro for a short spell while he was a Kosice player, with the Slovakian club giving him permission to travel to England for a trial.
Then Boro boss Gareth Southgate was impressed with what he saw but a deal failed to materialise and he would subsequently join the Blues.
"The club was okay, they were in the Premier League at that time with some good players like Stewart Downing and Robert Huth," he told Chelsea's official magazine.
"I don’t know why it didn’t happen – I went to join up with the national team and the clubs were supposed to talk, but I never heard any more about it.
"Who knows what would have happened if I signed for Middlesbrough – would I be here today? All I know is that I am a Chelsea player now and very happy to be here.
"I am 25 and I hope the best years of my career are going to be here."
Matic's presence in midfield has been one of the key reasons why Chelsea find themselves sitting atop the Premier League as we approach the final furlong of the season.
The former Benfica man attributes Branislav Ivanovic's role in helping to settle back into life in London for his seamless transition into the Blues setup.
"Branislav is a very good man," he added. "Everyone here likes him a lot and it is the same in the national team. We have lots of young players in our country’s squad and they look up to him like an idol. It’s good to have someone like him.
"We are only a small country, but for us Serbians I would say Branislav is a bit like David Beckham in England! In Serbia he is a king!"