Saunders is believed to have been in the market for a left-back for a number of weeks because he only has Stephen Ward currently fit and available to play in that role.
Having spoken with Liverpool manager Brendan Rodgers, Saunders confirmed that a deal to take 19-year-old Robinson to Molineux is as good as complete.
"We've more or less agreed a deal with Liverpool today," said told the club's official website. "I've spoken to Brendan Rodgers and we're looking to get Jack in for the rest of the season.
"He's a fresh face for us and is a good young player who is going to get even better as he gets older."
Robinson has made six appearances in all competitions for Liverpool this season.