Shiels is a Northern Ireland teammate of Davis' and said: "I knew once Rangers signed him, he would be a great asset to them.
"I think he could be one of the best players in this league and I think Rangers will do well to keep him permanently.
"From speaking to him, he is really enjoying it and he is pleased.
"He could not really ask for much more because they are going for all four trophies.
"I spoke to him last week, he is really enjoying it.
"He has settled in well, I think. I think they can keep him.
"Rangers are a massive club and they can attract the top players - he is one of them.
"Even if he does go back to Fulham, I think he will be going back with a bag of medals."