Briers, 34, has been missing since the 17-17 draw against Wigan in round two, and the Wolves have wobbled in his absence, losing four of their last seven games, including last weekend’s defeat at Leeds.
Smith told the club’s official website: “On the weekend it was one of those games when we could have done with Lee’s kicking game, although he’s not there at the moment and we need to take control of that ourselves.
“Having someone of Lee’s quality and experience coming back in the next little while will be great. He won’t be with us playing this weekend as he needs to do a bit more work; he hasn’t had as much physical contact training-wise as he needs so we need to get him up to speed on that and then he’ll get given the green light.
“Hopefully that may well be as close as the Keighley game.”
Warrington were drawn against Keighley in the Challenge Cup for the third year in a row in Monday’s draw, held at the Halliwell Jones Stadium.
They defeated the Championship side 44-18 at Cougar Park last season, having also beaten them 80-0 the previous year at home.