Wilkinson – Taylor’s first signing – has been out for more than a month after pulling his hamstring in training.
But the Saddlers expect to have him back soon.
When asked if the 26-year-old should return over the next few weeks, Taylor said: “Hopefully. That’s the plan.
"In the next few weeks, we hope to have Conor back training with the group.
“We’re pushing him along. He’s getting stronger in terms of the injury, so we’re hopeful that he’ll be back with the group and back with the squad as soon as possible.”
Wilkinson’s setback came just after he opened his Walsall account, sealing a 1-0 win over Stevenage.
Rory Holden and Liam Kinsella (both knee) remain on the sidelines with no time frames on their returns, while Ash Taylor is recovering from a hamstring issue.
On Wilkinson, Taylor added: “You’re able to take more risks with contact injuries as you understand it’s a coming together of players.
“But when a player has a muscle tear – and maybe it’s the first muscle tear of their career – you obviously have to be careful.
"Conor is getting much closer now, so we’re fortunate with that one.”