The former Liverpool boss succeeded Ronny Deila 10 days ago and has already moved into his office at the club's Lennoxtown training ground.
Rodgers, 43, revealed he invited captain Scott Brown, 30, to his London home for a discussion over dinner.
"It was good to get his opinion on how things are and how it looks for him at the club," Rodgers told Celtic TV.
"It was also good for me to introduce myself to him as the club captain and talk through my ideas and how I'd like to work.
"He's been here a long time, so he's been here through good times and tough times."
Brown's fellow Scotland international Charlie Mulgrew, 30, is out of contract at Celtic and revealed that Rodgers telephoned him to ask if he would stay for another season.
"I've spoken to a number of the players on the phone also," said Rodgers.
The Northern Irishman will have six weeks to prepare the Premiership champions for their first competitive outing, in the second qualifying round of the Champions League on 12 or 13 July.
"I'm really looking forward to 20 June, the first day back in and getting to meet all the players and talk through how we want to go forward," Rodgers added.
"That's when the hard work begins. It will be a long season, a hard season, but it will be really exciting. I can't wait to get started."

Richard Davies, 41, died of a single gunshot wound to the chest after firing at officers in St Neots, Cambridgeshire, in October 2015.
His widow Samantha said she had a text from her child saying they were tied up and begging her to "call the police".
Mr Davies was shot after firing a gun from the house. The inquest continues.
The father of three said he "wanted to end his life" after learning his marriage was over, the hearing in Peterborough was told earlier this week.
More news from Cambridgeshire
Giving evidence at the hearing, Mrs Davies said she had initially believed her husband had "some acceptance" about the end of their relationship and said "there wasn't an ounce of anger" during their conversation earlier that day.
However, he had made several trips to a nearby shop to buy alcohol and had been carrying a knife, the inquest heard.
Mrs Davies went to visit her sister and when her children returned to the family home their father tied them up.
The inquest then heard how the children managed to make 999 calls and alert their mother.
She received a text that read: "Call the police. Get them to come to our house. Dad's going to kill himself. He's tied us up. I'm not joking."
When Mrs Davies arrived, one child had managed to escape.
She said when Mr Davies came to the door "he didn't really look like my husband".
He returned a short time later with a knife pointed at his chest, she told the hearing.
Her other children managed to escape and Mrs Davies was taken to a neighbour's house.
Mr Davies was shot dead by a police marksman after firing six shots from the house, the inquest heard.
Mrs Davies said she had never seen his home-made gun or ammunition before, and her family was "forever changed" by what happened.
The inquest continues.

Cheteshwar Pujara and Ajinkya Rahane both hit centuries as India posted 622-9 declared in their first innings.
Sri Lanka were never in the game once they were bowled out for 183 in reply.
They managed 386 in their second innings - Dimuth Karunaratne making 141 - but India's spinners sealed victory on the fourth afternoon.
Ravindra Jadeja picked up the man-of-the-match award after hitting an unbeaten 70 off 85 balls at number nine before taking 2-84 and 5-152 with the ball.
India won the first Test in Galle by 304 runs. The third and final Test gets under way in Pallekele on 12 August.
Jadeja will miss that match after he was suspended for a breach of the International Cricket Council's disciplinary code.
The all-rounder pleaded guilty to the charge, which related to throwing the ball "in a dangerous manner" towards Karunaratne as he fielded off his own bowling on day three.
He lost 50% of his match fee and earned three demerit points, taking him to a total of six in the past two years, leading to a one-game ban.
New Celtic manager Brendan Rodgers says he has been discussing his future plans with some of his senior players.
[NEXT_CONCEPT]
The widow of a man shot dead by police has told an inquest of a desperate text sent by one of their children saying "dad's going to kill himself".
[NEXT_CONCEPT]
India completed a series win over Sri Lanka with a crushing victory by an innings and 53 runs in the second Test in Colombo.