"At the moment it would probably be Alan because he's playing well," Stimson told BBC Radio Kent.
"It's nice to have that competition and know the one who's in the shirt is performing so well you can't bring the other one in."
Royce has been on the bench for the last three games but Stimson confirmed he is not fit enough to start a match yet.
"He hasn't had a lot of goalkeeping because we've been travelling up and down the motorway," said Stimson.
"He's not far off it, but Alan has taken that competition on and the last few games has been really good."
Julian has played nine games since Royce's injury, conceding 10 goals, and has kept clean sheets in the last two home matches.
He had found opportunities limited after arriving from Stevenage in May 2008.
Up until Royce's injury he had only started eight league games for the club.
There's commentary of Gillingham's game at Brentford on Saturday 6 February 2010 on BBC Radio Kent 96.7 and 104.2 FM.
Source: BBC Sport
Source: BBC Sport