The pension fund looks set to beat buyout firms KKR, Apax Partners and Madison Dearborn, who also bid for the company.
Heartland, which is part-owned by Chicago-based private equity firm CHS Capital Partners, has EBITDA of about $120m.
It has more than 250 affiliated offices across 14 states providing business support for hometown dental offices including staffing, admin and IT support.
In September the dental practice management company hired investment banks to sound out buyers for a potential sale.
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