Reports have suggested that there has been discontent in the dressing room and that Liverpool legend Steven Gerrard has been approached over replacing Murty, and Rodgers feels that the Englishman has been "thrown to the garbage".
Kris Boyd says the Rangers job is a huge gamble for Steven Gerrard but with the correct backing he can succeed in Scotland.
It wouldn't be a surprise to see Rangers go in a new direction though, with Steven Gerrard rumoured to be on the verge of taking over.
The Liverpool U18s boss is scheduled for more talks this week, according to Murphy, and if he is given assurances over the money he will be able to spend then he will agree to succeed Graeme Murty.
"The truth is there's nothing definitive".
"He's a really ambitious guy Stevie, he always has been from the day he walked on to the training field at Melwood as a young lad".
The Ibrox club continue to find themselves well off the pace of Scottish champions Celtic, who emphasised the gulf between the teams with a thumping 5-0 Old Firm derby success on Sunday, which sealed a seventh straight title.
"I don't think he's going to put myself in a position where he goes into a job with his hands tied in terms of the resources."".
"I think he's probably needing some more reassurances".
And Gerrard is likely to press the Rangers board over the finances available to him should he take over a club who are third in the Premiership and level on points with fourth-placed Hibernian.
Asked if it was his best game in football, Edouard, speaking through an interpreter, said: "Certainly, I am going to remember this all my life because it is my first title". You have to think there's some credibility in what they are trying to do.
With the league won and the Hoops in holiday mode a 15 minute cameo would do Dembele the world of good, it would let him know just what you have to do to be involved in the first-team and it would let Rodgers know if the player should be added to the first-team squad more often next season.
"Go and get a taste of big crowds, big pressure, a local rivalry that is every bit as tense as Liverpool and Everton or Manchester United and Manchester City".