A Chicago-based private equity real estate firm is offering as much as $2 billion to purchase office buildings, health-care facilities, transit-related properties and whatever Hartford and Connecticut governments think they can sell, so long as the buyer gets a 7.25 percent initial return, plus annual rent hikes of 1.5 percent, Bloomberg News reported. The offer by Oak Street Real Estate Capital LLC, detailed in letters of intent delivered on Wednesday, leaves the choice of what properties to include up to the governments. Connecticut has been wrestling with an underfunded pension system and chronic budget deficits, in part because the national economic recovery has passed much of the state by, leaving it with fewer jobs than it had a decade ago. Hartford is even worse: The capital avoided bankruptcy last year only because of a bailout by the state. “I just want to see our state make a smart decision,” said Gregory Kraut, a managing partner of K Property Group who is also an elected member of Westport’s town government. “And with my real estate and financial background, I have some options for them.” Kraut, who put together the offer, said he’s acting as a concerned citizen and isn’t taking a commission or a fee from Oak Street. He suggested the state might use the money from real estate sales to reduce its unfunded pension obligations, and Hartford could reduce its debt load.