The 29-year-old was rescued from non-league obscurity by then-Oldham manager Dowie in 2002 and the pair have remained in close contact ever since.
Dowie told the Coventry Telegraph: "I was delighted to help Wayne make his transition back into professional football.
"People can misconstrue him but he is a tough boy with blistering pace and is certainly one we are looking at getting involved here."
Andrews was reportedly upset after being substituted by boss Gary Johnson after just 28 minutes of the Robins' recent triumph over Brighton.