England Under-19 striker Wright (pictured) appeared for The Foxes' reserves in midweek after an injury lay-off and was watched by Downes's assistant Garry Thompson.
Downes said: "We will continue to monitor Wright and I will be watching him myself.
"He was one of the targets we wanted before he got injured and could be a useful addition.
"Leicester manager Micky Adams would be willing to let him go out on loan to gain first-team experience."
The Griffin Park club have only managed four goals from their six Second Division games but have conceded 13, which may prompt Downes to keep his eye out for a defender as well if The Bees are to climb out of the relegation places.
