Adkins has had bids for Dawson rejected by the League Two leaders, but has now identified a new target ahead of the close of the transfer window.
"We have made another bid for a central defender and we will see what happens this week," Adkins told the Scunthorpe Telegraph.
"In the middle of last week, I thought we were getting close to an agreement, but towards the end of the week we did not seem quite so close.
"That's what things are like in the January transfer window. We have even suggested a loan deal with view to a permanent move."