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The 24-year-old was a subject of summer speculation following his impressive performances in Italy, with Monaco also reportedly interested.
However, Ghedjemis decided to remain at Frosinone and committed to the club by signing a new four-year contract.
According to Italian media, Celtic, Rangers, and Monaco had all shown interest in the winger, and Frosinone reportedly rejected bids worth around £8 million.
Ghedjemis has now shared that while he had ambitions of his own during the transfer window, Frosinone convinced him that staying was the right move. He said: "The summer transfer window? It's over.
(Image: Getty)
"I had my own ambition, but I spoke to the club, and they presented me with their new ambition of becoming a major club.
"I'm happy to have stayed and signed a new contract. Now I want to do well."
The Algeria international, who scored 15 goals last season as Frosinone secured promotion back to Serie A, is confident of continuing his impact at the higher level.
Discussing his personal targets, Ghedjemis added: "Would I sign to finish the season with 10 goals? No, ten goals is a great achievement, but I don't want to limit myself.
"I want to do my best."