The Toffees have already made seven signings this summer in the form of Gylfi Sigurdsson, Wayne Rooney, Michael Keane, Jordan Pickford, Davy Klaassen, Sandro Ramirez and Cuco Martina.
However, Koeman still wants to sign a new number nine to fill the huge gap left by the departure of Romelu Lukaku to Manchester United.
"We need at least two more players to get numbers in, but the most important thing is to get a striker in," Koeman said in his post-match press conference.
"If you look at all the squads of the big teams, they have so many options. If we get everybody back, like [Seamus] Coleman, [Morgan] Schneiderlin, [Yannick] Bolasie, [James] McCarthy... if we have them, that's good. But we have injuries, which are part of football as well."
Diego Costa has emerged as a surprising target in recent days after the Chelsea forward was deemed as being surplus to requirements by Antonio Conte at Stamford Bridge.
The Spanish international has been trying to force a return to Atletico Madrid throughout the summer but the two sides are yet to reach an agreement – despite Spanish radio station Onda Cero claiming last weekend that they were close to settling on a deal worth €45m (£41.6m, $53.2m) plus €10m in add-ons.
Recent reports have claimed that Everton could take advantage of the situation and sign Costa on loan, but Koeman was coy when asked if he could move to Goodison Park before the transfer window closes on 31 August.
"I don't know. We are looking to the players who are maybe available. If we sign somebody, it's somebody to make the team better. I don't speak about names of players. We are looking and doing our job. Hopefully we will arrange it for next week.
"I'm always confident because we did some good business, but the board knows the importance of the two signings."
Everton have been widely tipped to part ways with Ross Barkley this summer amid reports linking the England international with Tottenham Hotspur and Chelsea. However, Koeman suggested that the playmaker could stay with Everton yet to receive an offer for the 23-year-old wantaway.
"Until today [I expect him to stay] because we don't have any offer on the table for Ross," Koeman admitted.