Liverpool have suffered a poor start to the season that has left them marooned in the relegation zone with just two wins from nine Premier League games.
The club's ambitions in the transfer market were limited under previous owners Tom Hicks and George Gillett, but following the conclusion of a protracted takeover battle, Hodgson is hopeful he will be able to able to strengthen his squad when the window re-opens.
"If we want the right quality, we have got to be prepared to pay the right price," Hodgson told the club's website on Friday.
"The owners know that perfectly well. We have got to make certain that if we go out and spend 20 million pounds, we are getting a 20 million player.
"We want to be attracting the players that Barcelona, Real Madrid and Inter are chasing. It would be nice to think that we can shop at a high level."
Liverpool's poor form on the pitch was overshadowed in the early stages of the campaign by the boardroom wrangle that culminated in their takeover by New England Sports Ventures.
The change of ownership, however, has failed to end speculation in British media that high-profile players like striker Fernando Torres and goalkeeper Pepe Reina could be leaving Anfield.
The new owners, however, have hinted that top players will not be allowed to leave.
"I can reassure our supporters that we have no intention of allowing the team to be weakened going forward," NESV principal owner John Henry said on Friday.
