The cost of renovating an office building for Arlington County’s new homeless services center and 24-hour shelter is likely to cost about $5.5 million, county officials said Monday after they opened two bids submitted last month.

KBE Building Corp. said it would cost $5.7 million, and Miller Brothers Inc. bid $5.2 million, to remake two floors of 2020 14th Street. That’s in line with what the county expected, and the awarding of the bid is expected to go the County Board at its Feb. 22 meeting.

The “actual construction award will be slightly higher ... to reflect both project contingency and unit costs for some items,” a county spokeswoman said.

The county has set aside about $15 million for renovations for the entire building, including furniture, phones and non-construction renovation costs. Construction could start as early as March.

The purchase of the seven-story building, directly across the street from Arlington’s courthouse and police headquarters, cost $27.1 million a year ago. The proposal to turn the commercial building into county offices attracted some neighborhood opposition when it was first proposed in November 2011 because two floors would be devoted to housing single adults who are homeless.

The site is across two streets and a parking lot from the current winter-only homeless shelter operated for the county by nonprofit organization A-SPAN. It’s adjacent to high-rise condominiums and apartment houses in the Courthouse neighborhood.