The Norwegian defender has been a hit in the Premiership since his £2.5million move from FC Kobenhavn nearly a year ago.
“If a serious offer comes our way for Brede I’m pretty sure it’ll have to be considered,” said Hodgson.
“When the day comes we’ll have to take into account all the possibilities and probabilities and make a decision.
“But I would hope – and this might be a naive hope – that we could still keep him because he’s got a long-term contract with us here.
“I know he is happy here and happy with his football, so hopefully it hasn’t affected his thinking because I don’t know what he reads into that type of speculation.
“But at this stage we have absolutely no indication that Arsenal or any club of that stature are interested in Brede.”