McNamara is reshaping his squad ahead of the new campaign and will look at a group of trialists training with the club.
Striker Kudus Oyenuga had a loan spell at St Johnstone in 2012 and spent last season at Hayes & Yeading United.
Defender Calum Butcher, a team-mate of Oyenuga, and ex-Portsmouth winger Nadir Ciftci are also being considered.
The fourth man is Graham Carey, who is a free agent after the former Celtic midfielder left St Mirren at the end of last season.
Meanwhile, defender Sean Dillon has been appointed captain of Dundee United for the forthcoming campaign.