The Times claim both club and player are nearing an agreement having previously stalled over wages.
United are only willing to give the Spaniard, 29, around £75,000-a-week to stay on at Old Trafford.
However, Herrera is keen to stay on at United, recently saying: "All the memories I have are amazing.
“I’ve been able to win trophies for the club. I have been able to play more than 160 games right now.
“So what I have in my mind is to go for the 200 games and keep adding games for the club. And for myself.”
Herrera has played 171 times for Man United, scoring 18 times and laying on a further 25 assists since joining in 2014 from Athletic Bilbao.
However, Scholes claimed Herrera isn't fit to wear the famous United shirt earlier this week – saying he "can't play the simple ball".
Scholes said: "You have to question the quality of the player.
"Rio [Ferdinand] asked the question there when he said: 'Is Ander Herrera capable of playing that ball to Pogba?'
"Now, he's in 15-20 yards of space, it's probably a 30-yard ball – a simple ball – if he's not good enough to play that ball then he shouldn't be at this club."
Rio Ferdinand quickly agreed with his former team-mate too.
He added: "It is an easy ball and when you hear Paul Scholes say that… he was a player who could put the ball on a sixpence from anywhere on the pitch.
"But when you look at that pass it's not a difficult ball to play. I think it's confidence."
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