Metcalf jumped at a long-term offer from St George Illawarra after Tanah Boyd signed a contract extension with the Warriors, only for the starting No.7 to suffer a season-ending knee injury last round.
With Boyd sidelined, Metcalf missed his chance to tackle his new club on Saturday with Webster saying he hadn't trained while the Dragons paperwork was being completed.
Te Maire Martin has been named to partner newly re-signed Chanel Harris-Tavita in the halves.
The coach said Metcalf was still wanted this season but the club wouldn't use the NRL's 10-day cooling period to try to convince him to flip on his Dragons deal given Boyd's injury.
He said the 27-year-old's immediate playing future was in his own hands.
"It's up to Luke ... if we didn't want him to play another game for the Warriors he would be better off going now.
"He will be eligible for selection next week and if he gets back playing, he's a class player so it's up to him."
After announcing a one-year extension until the end of 2027 for Harris-Tavita, Webster said Martin was also a priority.
Veteran Martin came off the bench following Boyd's early injury for his first NRL match of the year and was key to the Warriors' thumping win over Brisbane.
"I've got so much confidence in him, like I think everyone's a little bit surprised at the way he played," Webster said.
"He's played 9-6-7-1, but his preferred position is halves and he's excellent at it and he did a great job.
"You've got to remember he was a halfback for Maori All-Stars and broke his leg and it's his second game back, so it's very impressive."
He also hoped to secure 30-year-old Martin, in his fourth season at the Warriors, beyond this year.
"He's got every opportunity to stay and he knows that," Webster said.
"We have no intention of letting Te Maire go but it's rugby league so we will see how it goes."
Meanwhile, Webster expects Jackson Ford to play like he has a point to prove against the winless Dragons after being overlooked for NSW State of Origin selection.
Ford has the most run metres of any forward in the competition with 1783, averaging almost 180 metres a game.
"I think it's pretty obvious he wanted to play, he's passionate about NSW," Webster said of the hard-running prop.
"He's also now probably very motivated, wants to play his best football, wants to continue winning here.
"Jacko will get back to playing the way he plays."
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