The 78-times capped Netherlands international, who won league titles as a player at Barcelona and Ajax, as well as a manager in Holland, was confirmed on Monday as successor to Mauricio Pochettino, who left to take charge at Tottenham Hotspur.
The St Mary's outfit face a difficult summer, though, with England internationals Adam Lallana and Luke Shaw among those attracting interest from the Premier League's elite and Saints fans worry that they will follow Rickie Lambert, who moved to Liverpool last month, out of the door.
However, Reed is optimistic that the arrival of someone of Koeman's status in the dugout will persuade those talents being targeted by top teams that Southampton have the ambition to match theirs.
"I hope the announcement will prick up a few ears and they will think that's a good positive move from the club," Reed told BBC South Today. "If players leave, it will be because we believe it is right for the club.
"We need to sit down, assess and audit our squad and look at the strengths and weaknesses. We'll look at players that we'd like to bring in and then look at the individual cases of the players who may want to leave."