The recapitalization of bailed-out insurer American International Group Inc is likely to close next week, a personal familiar with the matter said on Friday, as AIG shares touched fresh highs on news it was getting closer to the deal.

AIG said Thursday night its board had approved the issue of warrants to buy 75 million shares of common stock, which are conditioned on all the parties to the recapitalization agreeing it can close by January 14.

While that does not in itself guarantee the deal will close next week, it was one of the last key steps to finish the transaction. AIG said it will issue a statement on January 12 disclosing whether all the parties have agreed the deal can close by January 14.

A person familiar with the situation, who was not authorized to speak publicly on the matter, said the board's approval of the warrant issue showed the highest degree of confidence the deal will close next week.

Under the terms of the deal, the Federal Reserve Bank of New York will be repaid in full and the U.S. Treasury Department will be left with a 92.1 percent stake in AIG.

The government is contemplating two stock offerings this year to sell most of that stake, people familiar with the plan told Reuters last year. The rest would then likely be sold in 2012.

The source said Friday the company is targeting this March for the first share sale, but due to the complexity of the situation a sale in May was more likely.

Linus Wilson, a professor of finance at the University of Louisiana at Lafayette, estimated on Friday the taxpayers' paper profit on the AIG deal could come to $35.6 billion if the warrants trade at the price he expects.

AIG shares rose 1.9 percent to $61.58 in early trade, off earlier highs of $62.86. Through Thursday's close the shares were up 34 percent since the September 30 announcement of the recapitalization.

(Reporting by Ben Berkowitz; Editing by Derek Caney, Dave Zimmerman)