The Sun says the 29-year-old was all set to quit Old Trafford after talks slowed down over fresh terms.
But he is now poised to stay at United with negotiations taking an upward turn in recent days.
Herrera – out of contract in the summer – is expected to seal a new deal on a similar £100,000-a-week to his current wages.
An Old Trafford source said: “Ander is now ready to stay here after talks have been slow originally.
“The club have made it clear to him they want him to stay. They don't want him walking away on a free.
“He has a young family and is settled in the area. Ander is also really popular with the fans.
“It won't be too far different to the wages and deal he is on now. Everything looks to be heading into the right direction."