The Belgian champion moved to Quick-Step Floors in 2017, which allowed him to return to the cobbled classics. He is now one of the favourites for the Tour of Flanders after he placed second in Dwars door Vlaanderen and E3 Harelbeke, and won the Three Days of De Panne.
"He always conveyed a kind of restrained anger towards me," Gilbert told newspaper Het Nieuwsblad (opens in new tab).
"I never really understood why. Voilà, it's a fact. If you do not like someone, it can also serve as motivation.
"I never had the same feeling. I envy him if anything. His supporters have sometimes been very hard on me. After the Belgian championship, they behaved very negatively. But I don't want to cause problems. The respect between Greg and me is mutual."
The two raced together on the Lotto team before their time in BMC Racing's red and black colours.
"It wasn't always easy with Gilbert in the same team as we are the same type of rider," Van Avermaet said after winning E3 Harelbeke last week.
"It wasn't easy to make the right decisions in the team sometimes, but you see that Phil is a big champion, he gives it all when he rides with you, 100 per cent. If he was riding in my team, I couldn't jump after him, I can now."
Watch: Tour of Flanders 2017 essential guide
BMC generally only gave Gilbert a chance in the Ardennes Classics and let Van Avermaet lead their cobbled Classics team. This was one reason why Gilbert went to Quick-Step.
"That's why he made the choice to come to team Quick-Step," Quick-Step's sports director, Rik Van Slycke told Cycling Weekly. "He said, 'If I go there, I can do what I want to do.' He wanted to ride the cobbled Classics. We made a spot for him."
Gilbert added that if he won the Tour of Flanders (becoming the first rider from Belgium's Wallonia region to win the race since Claude Criquielion in 1987) it would be a team victory.
"I'm primarily Belgian," continued Gilbert. "I'm a competitive beast, I always want to win. I'd like to win, but I'd enjoy it as a team victory.
"That's just the difference from BMC. I was bored sometimes because I knew we'd ride for a sprint and we had nothing beforehand. But, I have no bad words about my previous employer."
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