The Shakers chief also revealed that star striker Andy Bishop has undergone a successful knee operation.
"I think we are close to signing a couple of players and we hope to announce them in the next week or so," Knill told the Bury Times. "It makes June a bit easier knowing that we are close to these signings and the pleasing thing about it is that we set out to get the two players we are close to.
"It's been easier to persuade players to come here this year because they have watched us on TV and want to be a part of what we have going here.
"We will probably start next season as one of the favourites for promotion and we are trying our best to push the club forward. If we do manage to sign these two players I will probably be looking to bring in a couple more and then take a look at some trialists in pre-season."
On Bishop, he added: "I spoke to him on Tuesday and he has come through it well. Hopefully he comes back for pre-season fully fit and ready to hit the ground running."