A Michigan businessman is leading an attempt to acquire McLean's Finalco Group, a financially troubled data processing and telecommunications equipment leasing company.

According to documents filed last week with the Securities and Exchange Commission, Harold Van Arnem, who runs a similar leasing company in Birmingham, Mich., has entered into an agreement to buy 10 percent of Finalco's stock from Lee Burnett of Colorado, and one third of the 44 percent stake in the company held by former chairman Jon Prager of Rockville. The agreement would bring Van Arnem's share of Finalco to 24.9 percent.

Van Arnem and two groups of Washington area investors plan to bring their stake in the company to 54 percent at a later date through the purchase of the remainder of Prager's holdings, and then make a public tender offering for the company's outstanding shares, Prager said.

The takeover, which is not considered hostile, would end a transitional period for the McLean firm, which has been under the interim management of Phoenix investment banker John Cotton since the resignation of Prager as chairman last December.

Finalco, founded 20 years ago, manages and leases $1.4 billion worth of equipment throughout the country and runs an equipment income fund that acts as a tax shelter for investers.

The firm was shaken in 1983 by a dispute with the IRS, which resulted in an estimated $2.5 million in lost earnings.

For the 1986 fiscal year, Finalco lost $1.7 million on revenue of $71.5 million. For the first nine months of this year, the company had a loss of $800,000 on revenue of $63.3 millio