The Brentford wide-man impressed whilst on loan at the Pirelli Stadium last season, scoring four goals in 24 appearances.
However, since he returned to Griffin Park he has been transfer listed and told that his future lies elsewhere, which has alerted the Brewers to the situation.
Brewers boss Paul Peschisolido has said "I'd love to sign Cleveland Taylor because he did a tremendous job for us last season, but if that falls through then we will need a right-sided midfielder,"
"Cleveland isn't wanted by Brentford, so I'd like to sit down with him and see if we can bring him here, but there are still talks to be had between Brentford and Cleveland before that happens.