The England international, who is currently at the World Cup on international duty, is heavily tipped to join former Saints teammate Rickie Lambert in making the switch to Anfield during the off-season.
Although Reed urges the 26-year-old to remain loyal to the South Coast club, with whom he has climbed the divisions, the Southampton chief hints that it will take a substantial bid in order to prise him away from St Mary's.
"Lallana's been here long enough, we've brought him to this level and we feel that perhaps he should give it a little bit longer," he told BBC Sport.
"Anybody seriously considering coming for our players is going to have to think very significantly about the size of the fee.
"If we do take money it will be because it's the right amount and it enables us to improve the team and move forward."
Lallana is contracted to the club until 2018.