The Dutch shot-stopper linked up with his former Swansea City boss in Glasgow in August, penning a two-year deal with the Scottish Premiership champions.
And speaking to Voetbal International, the 35-year-old revealed he has a good relationship with Rodgers, who wanted to sign him for Liverpool during his Anfield tenure.
“Brendan Rodgers and I have a good click, which was created during our time with Swansea City,” he said.
“Later as manager of Liverpool he tried to bring me to Anfield. Rodgers knows me as a goalkeeper and as a person, and believes that I can add something to his team.”
De Vries spent four years at Swansea, one of which was under the stewardship of Rodgers.
The Northern Irishman used Pepe Reina as his main goalie for his first season in charge on Merseyside, before signing Simon Mignolet from Sunderland to replace the Spaniard in 2013.
De Vries was potentially eyed as a back-up option, with both of the aforementioned goalies having had only Brad Jones for serious competition.
The veteran stopper has made two appearances for Celtic since joining them from Nottingham Forest during the summer.