Learn English – Phrase for always watching for something better

idiomsphrase-requests

There's an idiom for never being satisfied with what you have and always looking out for something or someone better, particularly in reference to dating. The phrase is something like

Keep one eye on the door

referring to watching the door for the next new hot person to walk in the room.

My google searches have not resulted in any hits, which make me believe that I don't have the wording quite right. Does anyone know what this phrase is supposed to be?

Best Answer

There is a phrase that captures the idea perfectly, although it is not exclusively used for dating: Always chasing rainbows.