Johnson told BBC Radio Cambridgeshire: "We've got two or three offers out there and we're hoping for a pretty quick response.
"We've got Dave Hibbert on board, he gives us another option up front and that's a very pleasing start."
Posh have been strongly linked with Scunthorpe midfielder Grant McCann, but Johnson has refused to confirm that talks have taken place.
We've still got Shaun Batt and he's done very well at Millwall, but I would definitely like a fourth striker
Gary Johnson
However he is waiting to hear from a number of players after making contract offers.
"I'm pleased with the players we've spoken to and I think they are happy with us," he said.
"But these players need to make sure they make the right move for their families and their football careers."
Johnson said he wants at least two players for every position and has admitted that he is still looking for another striker.
"We've still got Shaun Batt and he's done very well at Millwall, but I would definitely like a fourth striker," he said.
Meanwhile, the Posh boss said they are yet to receive any firm offers for Craig Morgan.
The 24-year-old centre-back has been linked with a move to Preston to link up with former boss Darren Ferguson.
"We've had no official offer from Preston so until we have a figure on the table it's all just speculation," he said.
Source: BBC Sport
Source: BBC Sport