Kinnear told the Nottingham Evening Post: "I want to bring in players who are equally as good as Michael Dawson and it is difficult.
"I am looking at international centre-halves and I will be travelling to Brondby on Sunday."
Forest are currently without John Thompson (shoulder), Michael Dawson (groin) and Wes Morgan (suspension) which leaves the Reds with only Chris Doig as a recognised centre-back.
Jon Olav Hjelde played in the pre-season defeats against Middlesbrough and Tottenham and could earn himself a year's deal this week.
Forest have supposedly enquired about Southampton's David Prutton in a loan deal but it was rejected by Saints manager Paul Sturrock who sees the former Forest midfielder as a useful squad member.