Djokovic has been living in the shadow of Federer and Rafael Nadal over the last year but he finally returned to his best when winning Wimbledon in July.
He then beat Federer in the Cincinnati Masters final before going on to win the US Open.
The pair were team-mates as Team Europe secured a dramatic Laver Cup victory against Team World last over the weekend.
And now Federer, 37, is hoping the can continue challenging the Serbian for the top honours as he looks to cement his place as the greatest player of all time.
“I have enjoyed spending time with Novak,” Federer said.
“I said it in the beginning that we have had an intense rivalry over the years.
“I always thought we got along well and respect each other on and off the court but being able to support him, him supporting me, going through that process and talking tactics, talking team, talking who should play and just seeing what a leader also Novak can be, it’s been really nice and refreshing for me.
“I won’t say it’s going to rejuvenate our rivalry, and I hope we will play many more times, but it’s been nice on many levels.”
Federer and Djokovic lost 6-7(5), 6-3, 10-6 to Kevin Anderson and Jack Sock as they played doubles together for the first time on Friday.
Djokovic also lost to Anderson in the singles as Federer beat Nick Kyrgios.
The competition went down to the final match of the weekend for a second year in a row – in which Alexander Zverev defeated Kevin Anderson 6-7(3), 7-5, 10-7.
And after lifting the Laver Cup, Federer was delighted with the victory.
“I’m not sure if I wanted it to be that exciting! What a match, what a weekend,” he said.
“Thank you Chicago, that’s it. I can’t thank you enough.
“The Laver Cup is here to celebrate tennis and have a great weekend and for everyone to enjoy themselves.”