The Saddlers are reeling after a 3-1 defeat to Harrogate Town and had Hayden White pick up a fifth booking of the season, meaning he will miss this Saturday's clash with Rochdale through suspension.
They have been boosted, though, by the progress of both Kinsella and Wilkinson, who were due to join in with the group at Essington today.
Taylor is excited to see them back in action and also hopes to have Rory Holden and Zak Mills fit again soon.
When asked about Kinsella and Wilkinson, and the injury situation as a whole, Taylor said: "Liam and Conor are back with the group. They're desperate (to be involved).
"Even when they come out of the treatment room, we've still got Zak and Rory in there.
"We need to empty that treatment room as quickly as possible, because there's too many players in there that can affect the team who haven't been available.
"It's through no fault of their own, of course. Injuries are a by-product of the game we play.
"I know the lads who will be back with the group now have worked extremely hard – and Rory and Zak are doing the same.
"We've got an extremely good medical department here and the boys will be back as soon as possible for that, I'm sure."
Meanwhile, Taylor says Walsall are in for a hard week of training – but not as a direct punishment for their shortcomings against Harrogate.
"We'll work hard, but it's not a punishment," said Taylor.
"We work extremely hard every week. There's no punishment, but what we need to do is work hard all week.
"We'll dissect the reasons we lost and look forward to next weekend."