Should it choose not to make an offer by the 5 March deadline, Global will be prohibited from making an offer for six months.
The Takeover panel said: "By 5 March, Global Radio will have had more than 11 weeks since its initial approach and more than three weeks since Fru Hazlitt's presentation of her plans for the group to make a decision."
The notice challenges Global, chaired by Charles Allen, to make a move for GCap within five weeks.
Global Radio first made an approach over a potential takeover in December, offering £313m for the company. However, GCap rejected the offer immediately.