The Blues were frustrated in their push to sign Balogun - with the USA international reportedly unhappy with how he was treated during his medical at the Hill Dickinson Stadium - as Moyes wrapped up deals for Ainsley Maitland-Niles and Jack Grealish.
The lack of attacking options has caused concern for Everton fans with Beto and Iliman Ndiaye also moving on.
As per reports from talkSPORT, a last minute deal to sign former Manchester United star Anthony Martial fell through, but Moyes could revive that link the coming days.
Martial is a free agent - and can join a new club outside of international transfer windows - following his exit from Mexican side Monterrey earlier this year.
The 30-year-old scored 63 goals and laid on 33 assists for the Red Devils across 209 games in nine years at Old Trafford, but there are concerns over his fitness levels, and Moyes may only offer a deal until the end of the current season.