Everton face losing both Romelu Lukaku and Ross Barkley to Premier League rivals at the end of the season.
Express Sport understands Lukaku wants a move back to Chelsea, who are willing to spend up to £70m on the Belgium international.
And with Arsenal and Tottenham both reportedly interested in £30m-rated Ross Barkley, Koeman is wary that he will need new players arriving for next season.
Romelu Lukaku not impressed at Everton training ground
Wed, March 15, 2017
Click through the gallery to see Romelu Lukaku's day at the Everton training ground
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Click to reveal snaps of Romelu Lukaku's day at the Everton training ground
According to the Daily Mirror, Koeman wants billionaire owner Farad Moshiri and chairman Bill Kenwright to hand over every penny made from player sales, so the cash can be reinvested in the squad.
Koeman would ideally like to keep both players but is said to be realistic about those chances.
The Toffees manager will also have leeway in Everton’s wage bill to handsomely pay whoever comes in to replace the duo.
Everton owner Koeman wants Moshiri and Kenwright (right) to grant him £100m in transfer funds
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Belgium's Romelu Lukaku could leave Everton for Chelsea this summer
Ross Barkley is currently away on England duty
Lukaku has rejected a £130,000-a-week contract, while Barkley signed a £65,000-a-week deal in 2014.
It has emerged that Everton are interested in signing Lazio defender Stefan de Vrij, whose contract also expires next summer and who is valued at £30m.
Other Everton targets include Burnley’s Michael Keane and Manchester City’s Joe Hart.