Bailly had an impressive first season at United after joining them from Villarreal in a £30m deal.
The Ivory Coast international made 38 appearances helping United win the League Cup, despite missing six weeks of the campaign with a serious knee problem.
Bailly would have also started in the Europa League final win over Ajax if he hadn’t been suspended.
United have struggled to replace the likes of Ferdinand and Vidic since the duo retired.
But boss Jose Mourinho reckons Bailly is the man to do it.
The 23-year-old believes he is capable of emulating two of United’s greatest-ever defenders and go on to be ranked alongside them.
He said: “They are players in which I cannot do exactly the same as they did, but I have to try to follow in their steps.
Pierre-Emerick Aubameyang (Gabon, Borussia Dortmund)
“They are players in which I cannot do exactly the same as they did, but I have to try to follow in their steps”
Man Utd ace Eric Bailly
“It is very difficult but everything is achieved with hard work, and I hope that happens in my case.”
Mourinho has had a penchant for warrior-like centre backs at his previous clubs, including the likes of John Terry, Marco Materazzi and Sergio Ramos, who was Bailly’s hero growing up.
United fans reckon Bailly is built in the same mould and he said: “They are big players which you have to have a lot of respect for.
“You always have to have an example like them to try to be like.
“Once I started growing up and seeing professional football was a step closer, I would look at Sergio Ramos. I always looked up to Ramos as an example and watched him a lot.”
Bailly comes from a humble upbringing in the southern city of Abidjan where, amongst other jobs, he repaired phone boxes as a child to earn some much-needed cash.
He admits he was left shocked when he discovered United were willing to spend £30m on him.
“As a child I started working,” he said. “I had a program after training in the afternoon in which I would go in front of my house to do various things.
“The phone boxes was something I did to earn some money. I couldn’t always rely on my parents.
“My dream was like all the other kids to get to the best possible level – which means professional football.
“I have made that dream come true thanks to god.
“I found out when I was in the Ivory Coast about the move to United and I didn’t believe it was true. I thought it was a dream.
“Afterwards I found it was true that the team was interested in me and it was something big for me, and I am thankful for everything that happened in that moment.”