Andrews joined the Baggies on a six-month contract in January after having left Blackburn.
Hodgson said: “When we signed Keith it was a case of seeing where the club is in the summer and then we will review the situation.
“It was a case of if things go well for him and the club then there was no reason to ‘divorce’ and, if the club didn’t do well or he didn’t settle, then he would be a free agent again.
“At the moment we look very much on track to achieve our goal (of staying in the top flight).
“Between now and the end of the season, we will look into contract situations with people like Keith who could walk away. I’m sure we will be sitting down to make sure that doesn’t happen.”
