The speculation was always likely, perhaps, once the Saints clambered up the Premier League to an early third spot, and it became inevitable after they smashed sorry Sunderland 8-0 last weekend.
Add to that mix Koeman winning Manager of the Month and his star striker Graziano Pelle scooping Player of the Month, and it blends a potent mix of hope and expectation, if not quite south coast hysteria.
"Dreaming is not bad," Koeman told reporters at St Mary's Stadium. "Because always you dream about the best and something nice and OK, we are in a good place now.
"But it cannot be a conclusion after eight games. It looks like Chelsea and Manchester City are the strongest but we will see.
"Yes, maybe there could be a surprise in the top four -- if you believe, everything is possible."
Koeman, a stalwart of the great Dutch sides of the 1980s and 90s, knows better than anyone, however, that belief alone won't win prizes.
Experience counts for a lot in the cut and thrust of England's top flight, and that is an area where Koeman has concerns.
"The difference is they have 24, 25 players already prepared to play Premier League," Koeman said of the big challengers, the Chelseas, Arsenals and Manchester clubs.
"And teams like Southampton don’t have that. We have some young players. Maybe they will get the chance, but they don't have the experience and you're not sure about the level, the Premier League level, that is the difference."
Koeman has already identified one area where he would love to build some experience by making the loan signing of Chelsea left back Ryan Bertrand permanent.
Saints have the option to sign the player and Koeman said that if finances allow he would like to see Bertrand join full time.
"If we have the money, yes," he said. "If it's up to me, yes."
Southampton, third on 16 points after eight games, host 10th-placed Stoke City at St Mary's Stadium on Saturday.
(Editing by: Mitch Phillips)
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