Rodgers, who was appointed the Celtic manager in the summer of 2016, was in charge of Premier League club Liverpool from June 2012 until October 2015.
Deila was the Celtic manager for two seasons between 2014 and 2016. The 41-year-old Norwegian won the Scottish Premiership title twice and the Scottish league Cup once during his spell at Celtic Park.
The former Celtic boss has revealed the conversion he had with Rodgers when the latter was at Liverpool.
“I see Brendan as a very-respectful guy and I went to Liverpool to meet him before I was Celtic manager," Deila told The Daily Record.
“I’m not sure he’ll remember me, but there were a lot of same thoughts about developing people when we sat down and spoke.
“When I was leaving, there was one sign I remember which hung as you walked out of the building and it read: 'Have you been better today?' That is a culture which I tried to build when I was in Celtic.”
Celtic will return to action on Sunday afternoon when they take on Old Firm rivals Rangers at Hampden Park in Glasgow in the semi-finals of the Scottish Cup.