"We are looking for a left-footed central defender, maybe as back-up for Leighton Baines," Koeman told Sky Sports following Monday's 1-1 draw at Manchester City.
"With the injury to Funes Mori we don't have any left-footers on that side as a back-up for Leighton.
"Also a striker because I think even with the talent of Dominic and Ramirez, look to other squads. They have that number of players. If we need to make the next step we need a striker in as well."
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Rooney's 200th Premier League goal put Everton ahead after 35 minutes before Kyle Walker was sent off on his home debut for City just before the half-time.
City equalised following a late goal from substitute Raheem Sterling before Everton midfielder Morgan Schneiderlin was shown a red card.
"We had problems with keeping the ball and we played too fast the long ball. We worked really hard for the result, and one point is a good result," said Koeman.
Everton, with a 2-0 lead, visit Croatian side Hajduk Split for the return leg of their Europa League playoff on Thursday before visiting defending Premier League champions Chelsea on Sunday.
(Reporting by Hardik Vyas in Bengaluru; Editing by Peter Rutherford)
