McCarthy's £500,000 move for Lallana has been branded "derisory" by Saints boss Mark Wotte, says the Daily Star.
McCarthy was hoping to snare highly-rated Lallana, 21, at a knock-down price following his £1.2m acquisition of Andrew Surman amid Saints' financial uncertainty.
Midfielder Lallana has refused to play in any of Southampton's pre-season games after telling Wotte he wants to leave the League One club.
Wotte said: "There is some interest for him and he would like to join a club in the Championship or Premier League.
"But as I have said before, we are not going to sell Adam Lallana for a cheap price. He is a quality player.
"So if there is a club interested they have to do serious business and not try to take advantage of the situation."