From Longman Dictionary of Contemporary Englishhave your eye on somethinghave your eye on somethingWANTto want something that you think might become available He has his eye on the bigger apartment next door. → eye
Examples from the Corpus
have your eye on something• As I told you, I have my eyes on a very different sort of market.• He must have his eyes on a Ryder Cup spot.• Rodrigues has his eye on the major leagues.• A few years more and white men will be all around you. they have their eyes on this land.• We have our eyes on a nice little house near the beach. 