Southampton executive director Les Reed hopes Adam Lallana will commit to the club now Ronald Koeman has been confirmed as their new manager.
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Koeman took over at St Mary's on Monday following Mauricio Pochettino's departure to Tottenham and the Dutchman is already aware several of his star players are seeking moves to bigger clubs.
Along with defender Dejan Lovren, Lallana has been subject to reported interest from Liverpool but Reed has urged the England international to stay at Southampton.
"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," Reed told BBC South Today.
"Anybody seriously considering coming for our players are 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."
Koeman and brother Erwin, who was announced as his assistant, must work quickly to resolve the future of their key players and it is understood Ronald will take English lessons ahead of the club's pre-season campaign.
Striker Rickie Lambert has already completed a summer move to Liverpool, while defender Luke Shaw has been heavily linked with a move to Manchester United. Koeman ultimately wants to steer his new club into Europe and, while he could not give assurances, wants to do everything he can to keep his star players at St Mary's.
"We know all about the rumours. The club and I will do everything to keep the best players, but finally that is the decision of the club," Koeman said.
"We need to continue what they [Pochettino] did, maybe to reach some more, to win prizes. Maybe one day to play in the European Cup, I think that has to be the next steps for Southampton. We will do that with everybody. That is important."