The 23-year-old joined Celtic on loan from Norwich City in January and has since scored nine goals across eight starts and eight substitute outings in all competitions, netting his most decisive goal at Hampden Park to help the Hoops complete a domestic double.
After a lacklustre and nervy first half, Rangers thought they had taken the lead when half-time substitute Abdallah Sima kneed the ball over the goalline after a corner, but Nicolas Raskin was deemed to have pushed Joe Hart in the build-up by VAR.
That proved to be a turning point and Rangers' attacking efforts were ultimately in vain, as Scottish Premiership champions Celtic snatched victory in the 90th-minute when Idah pounced on a loose ball, parried into his path by Jack Butland, before firing home from close range.
Idah's contributions at Celtic during the second half of the season have been praised by Rodgers, who has suggested that he keen to sign the striker on a permanent basis.
Rodgers salutes "absolutely immense" Idah impact
"The board know how I feel on Adam, that was the reason for bringing him in," Rodgers told reporters after the match. "He's been a real catalyst for us, especially over the last few months.
"I knew what I was getting because I'd seen him in the Premier League at 18. He has all the attributes. He's fast, dynamic, strong and I felt with better positioning he'd get goals.
"What he's done since coming in is show that he's a goalscorer. He gets different types of goals.
"He has great movement in the box and he deals with pressure moments. Today, he was like a real number nine sniffing in and around the box.
"He's been absolutely immense for us and he's clearly someone I'd like to do something with.
"I've seen development in him and that's what the game's about - players improving. I just know with Adam that he's got such a high ceiling."
Rodgers remains coy on future of "big-game player"
Rodgers added: "The Premier League is the most competitive league in world football and you need a certain level of physicality and he showed that as a really young player.
"Adam probably got lost a little bit for a few years but coming to here, he's thrived on the pressure of being at a big club.
"He was clear on his role when he came in and how I would use him. Adam had to get a feel for us but I told him he had to be ready to make an impact, either starting games or coming on.
"His confidence has never wavered, he's been a brilliant team player for us. He's such a good guy, the players love him. And he's a big-game player. In so many big moments, he's stepped up to the plate for us.
"My talks with Adam will remain private because there's a lot of work to do, but he knows my feelings and so does the club so we'll see what happens."
Idah came through the youth ranks at Norwich, making his senior debut in 2019, and has since made 115 first-team appearances for the Canaries in all tournaments, scoring 17 goals including six in the first half of this season.
As things stand, the Republic of Ireland international is set to return to Carrow Road, where he is under contract until the summer of 2028.