(Corrects paragraph 3 to read "almost what" instead of "more than")
MADRID, May 23 (Reuters) - Spain's Caixabank may sell around 10 percent of Grupo Financiero Inbursa , a Mexican bank controlled by tycoon Carlos Slim, in response to renewed pressure to shed investments and bulk up capital.
A sale of the stake, worth $1.6 billion, would reduce Caixabank's holding by half and bring in a sizeable profit if it sold at current market prices.
The 10 percent stake is currently worth almost what Caixabank paid for its entire 20 percent holding in Mexico's sixth largest bank by assets in 2008.
The Spanish bank declined to comment on the capital gain it is expecting from the Mexican sale, only adding that the deal was dependent on pricing and market conditions.
The Slim family has the first option to buy back a stake if sold, according to the prospectus for the original 2008 deal.
Inbursa said on Thursday it would hold a share offering on behalf of Caixabank.
Caixabank said the sale would not harm its relationship with Inbursa and its main backers, family of billionaire Slim family, which owns 56 percent.
The Barcelona-based lender paid around 1.5 billion euros in 2008 for the 20 percent stake and has close business ties with Slim and Inbursa, including on the technology front.
It also signed a 428 million euro sale and leaseback agreement with Inbursa on a clutch of properties late last year.
"The board members we have at Inbursa will continue to be there, for example," a source at Caixabank said. "This doesn't affect our good relationship with the group, the good relationship is in part what makes it possible (to do this)."
Caixabank, like Spanish rivals, needs to strengthen its finances this year to cope with higher provisions on bad loans. The country's banks are also reinforcing their capital after a 2008 property market bust.
Caixabank is also looking to sell at least some of its corporate holdings as stricter international rules on capital make it costlier to keep them.
It has chunky stakes in Spanish companies such as Telefonica , Repsol and Gas Natural, though not many of its investments have done as well as its Mexican venture.
Shares in Caixabank, Spain's third-biggest bank, were up 1.3 percent at 1130 GMT, reversing losses earlier in the day.
Caixabank, the commercial banking business of financial services group La Caixa, was one of the biggest buyers of failed banks.
Inbursa's shares closed at 29.38 Mexican pesos ($2.38) on Wednesday. They have risen over 60 percent since 2009. ($1 = 0.7766 euros) ($1 = 12.3328 Mexican pesos) (Reporting By Elisabeth O'Leary, Jose Elias Rodriguez and Sarah White in Madrid and Simon Gardner and Michael O'Boyle in Mexico City; Editing by Erica Billingham and Jane Merriman)