Jessica Simpson and Jeremy Renner appear to be flirting on Instagram, but is he the right fit for the pop star?

Jeremy Renner, Facing 'Long Road to Recovery,' Is ... he is a fighter and doesn't mess around," sister Kym recently told PEOPLE about her brother's progress. "He is crushing all the progress ...

RELATED VIDEO: Jeremy Renner Speaks Out for First Time Since ... his sister could be seen massaging his head and making her brother laugh as their mother looked on during what the actor wrote ...