40-year-old Colombian singer, Shakira and Spaniard Center back, Gerard Pique, 30, has reportedly ended a 6-year-old relationship which saw the couple having two kids.
Argentina are in danger of missing a first World Cup since 1970 after being held to a goalless draw by Peru.
Only the top four in South American qualifying are guaranteed a place at the 2018 tournament in Russia, and Argentina are sixth with one game left.
The two-time World Cup champions must win their final qualifier in Ecuador to claim at least fifth spot which sets up a two-leg play-off against New Zealand.
The final round of games kick-off at 00:30 BST on Wednesday, 11 October.
The Spain international, 33, has made 639 appearances for the Catalan club - second on their all-time list - and scored 55 goals. Iniesta came through La Masia, the Barcelona youth academy, after joining in 1996 at the age of 12.
He made his first-team debut in October 2002 and has won eight Spanish league titles and four Champions Leagues.
Iniesta has captained the side since 2015 and shares the record with Argentina forward Lionel Messi for the most titles, 30, in Barcelona history.