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The five-time European champions are in advanced talks with a number of potential buyers that could see Hodgson being handed a large sum of money to spend on strengthening his team. One of those suitors is reported to be backed by the Chinese government.
But even if he is given the green light to go out and spend big, Hodgson does not envisage he will have enough time to invest huge sums in the current window, which closes at the end of August. "If and when a takeover is about to happen then I'm sure I'll be informed," said Hodgson.
"It would be nice if one day an enormous amount of money is made available. But we would have to make sure we do our research on each and every player we sign.
It is important to check the backgrounds and the character of everyone we sign. We've brought in Danny Wilson and Joe Cole since I arrived and I hope to bring in another of couple of players."
One player Hodgson does hope to sign in the coming days - takeover or no takeover - is Juventus's highly-rated midfielder Christian Poulsen, who played under Hodgson at FC Copenhagen.
Hodgson was speaking after getting off to a winning start in his first home game in charge of Liverpool since taking over from Rafael Benitez.
First half goals by David Ngog and, from the penalty spot, Steven Gerrard saw off Macedonia's Rabotnicki on Thursday as Liverpool coasted into the play-off stage of the Uefa Europa League with a 4-0 aggregate.
The match also marked Joe Cole's first competitive match for his new club at Anfield. And the former Chelsea midfielder impressed with Cole denied his first goal for his new club by the woodwork. "Joe came here because he thought he would have more opportunities to start games than he would had he stayed at Chelsea," said Hodgson.
"He's very enthusiastic and wants to play every minute of every game. We saw that in this game and we'll see it throughout the season."
Hodgson saluted the performance of his team against Rabotnicki. "A quality performance, it's a long while since I have seen quite so many goal chances created," he added.
"I'm sure the next round will be a bit tougher. We are always learning about the players here. The thing I have learned most is that their attitude is so good."
Defender Jamie Carragher said that Hodgson was beginning to make an impact at Anfield.
"We've said goodbye to Rafa and wish him well at Inter Milan, but Roy has come in with his ideas and we're enjoying ourselves. There's definitely a bit of a buzz about the place," said Carragher.
