Fletcher's future has been subject to discussion since he guided Argyle to safety with the initial deal only lasting until the end of the current season.
But Brent has been impressed with the former Pilgrims midfielder since taking the helm and hopes he can bring success to the club.
"Hopefully we'll reach an agreement. We're in discussions about Carl and the management team staying, they're reasonably advanced," Brent told BBC South West.
"We have been approached by a number of senior football managers - but the ambition is to clearly to carry on with Carl and his colleagues.
"We want to compete to win next season, we don't want to compete to stay up. We're aspiring to succeed."