But Everton have been linked to a number of other high-profile players this month and Murphy expects Sam Allardyce to sign more players before the window shuts.
"It's finding that balance now for Everton," he told BBC Sport.
"You don't want to be too attacking and leave yourself wide open again and go backwards – but Sam won't let that happen.
"He's good in the transfer market isn't he? I expect a couple more to come in."
If things to go plan then Tosun could be an outstanding signing for the Goodison Park side.
The 26-year-old managed 41 goals in 96 games for Besiktas but that doesn't quite reflect his growing prowess as one of Europe's top strikers.
Thirty six of those goals have come in the last 18 months or so, and his record of four goals in five Champions League games this season should illustrate that he isn't just prolific against Turkish sides.
Everton have struggled in a big way since losing Romelu Lukaku but hopefully for their sakes Tosun can be an apt replacement.