"Envious eyes" refers to the expression of jealousy or longing that someone's eyes display when they desire something another person has. Full definition
Overseas organizations have also cast envious eyes on another Australian resource — its young scientists. (sciencemag.org)
Proximity dictates that it was not a popular move among supporters of the former but these two clubs have bigger fish to fry in terms of rivals — both are currently casting envious eyes towards the Premier League, to Blackpool and Blackburn Rovers respectively. (thetwounfortunates.com)
I think we've all looked with frankly envious eyes at the success of the Newbery and Caldecott Medals, for example, and wished for something on that scale honoring adult books. (bookpage.com)