Hodgson has confirmed Babel was almost sold on transfer deadline day last month - with West Ham and Tottenham rumoured to be interested - but he could not find an adequate replacement in time.
Now he has told Babel, 23, he will be given a chance to deputise for Fernando Torres in his preferred central striking position. However, the Reds boss, who has some sympathy for the Dutchman in terms of how his Anfield career has failed to flourish, has warned if he does not come up to scratch there is a chance he will be replaced.
"The thing about Ryan is that for three years here he has not had much of a look-in,'' said Hodgson. "He was brought into the club with a lot of pomp and ceremony after winning the European Under-21 championships. I saw him play several times because I was working for UEFA at those championships and he was the player who was being chased by clubs all over Europe at that time. Since coming here he has not fulfilled that potential, hasn't had the chance to.
"So when there were offers for him (in August) we were prepared to allow him to go down and speak to those clubs. But we made it perfectly clear that other things would have to slot into place before we were able to allow him to go. The other things we had in mind did not slot into place and now it is up to him to convince me. No doubt if, by January, he hasn't succeeded in convincing me that he is the player we need then he will have to accept we will be in the transfer market for a centre-forward once again.
"But at least he has this period of time. He is working very hard, he is very determined to take this chance he has got so that last-minute transfer thing was perhaps something we will all be glad did not come about. In the meantime we will have the chance to do our thorough scouting so if money was available (in January) we would be able to look into the situation again.''
Babel has been infuriatingly inconsistent in his three seasons at Anfield since arriving from Ajax for £10.5million having been one of the stars of the 2007 European Under-21 Championships. He has scored some important goals for Liverpool in that time but they have been all too infrequent and his work-rate and commitment have regularly been called into question.
In his defence the Dutchman has suffered from being posted out on the left wing by former manager Rafael Benitez for the majority of his time in a red shirt. Hodgson is prepared to give him a go up front as he looks to ease the physical burden on Torres, but the player needs to deliver when he gets the chance.
"I am more than happy to work with Ryan but I haven't seen enough of him,'' said the manager. "He came back very late from the World Cup so I've worked with him for three or four weeks and he has done very well, applied himself well and he obviously wants to immerse himself into the type of work we are trying to do - which is very commendable. But it is far too early for me to have a strong opinion on him as a player, especially since he has been at the club three years and people have made judgments on him.
"As far as I am concerned it is a fresh start for everyone at the club. It is a chance for him to wipe the slate clean and show what a good player he is and there will be opportunity to do that. At the moment I can't ask any more than he is doing but I am not prepared to make any bold statements about him until I know him better and have seen him in some games.''
Hodgson, linked with the England manager's job post-World Cup before he took over at Anfield, refused to answer questions on who should be Fabio Capello's successor. This week the Italian, whose side have won their first two Euro 2012 qualifiers, confirmed he would not be staying on beyond the European Championships.
"My job is at Liverpool and I'm very happy with my job,'' said Hodgson. "I would like to make it very clear I have no intention of making any comments on the England national team other than to congratulate them on their last two results. I am looking forward to my job here.''