The Bairns boss was hopeful of getting his target tied up by the weekend and said: “It would be a great signing for the club.”
McKinnon wouldn’t confirm the identity of the player, but it’s thought to be someone of experience who played in the Premiership last season.
Meanwhile the Bairns boss got his first look at the players he has already brought in in a match environment.
Falkirk took on Hamilton Accies in a behind closed doors bounce game at their Stirling University pre-season training base.
Accies won 2-0 with a double from Marios Ogkmpoe - but like most managers McKinnon won’t read too much into pre-season friendlies.
The aim is to bring on fitness and match sharpness, and from that point of view McKinnon was delighted with the exercise.
He said: “I thought it was excellent, we played some great stuff. Everybody got 45 minutes and we had a lot of trialists in as well, so it was good.
“For the first game the fitness was very good so I’m very happy.”