Maynard, who moved to Ashton Gate from Crewe in a ?2.25million deal in July 2008, still has a year remaining on his current contract but the Robins are keen to secure his long-term future.
The 24-year-old scored 21 goals last season and has netted six times in his last eight games since returning from a long-term knee injury in February.
"Nicky's happy to be back playing again, fit and scoring goals and we're delighted to have him. There's discussions going on, like there is with a few players," Millen told the club`s official website.
"I don't want to leave everything to the summer. We know what we want to do and that's what we're getting on with."
Millen revealed one of those other players is veteran defender Louis Carey. The City captain, who is set to resume training after suffering a fractured skull in February, is out of contract in the summer.
Source: PA
Source: PA