According to Samuel Luckhurst of the Manchester Evening News, with both players' deals set to expire at the end of the season, United are concerned about the prospect of the two Spaniards speaking with clubs from overseas in January, with a view to agreeing a pre-contract.
As such, it's reported United have started negotiations with both players' representatives over possible new deals.
Per Luckhurst, Mourinho recently said he was hoping that Mata and Herrera would agree extensions.
"I hope they will stay," said the United boss. "We had a similar conversation last season about Marouane [Fellaini] and I was always saying I hope he stays, I believe he stays. I say the same. I hope they stay. Of course, I am happy with the players."
So far this season, neither Mata nor Herrera have been regular first-team players for United, but at times they have shown they still have something to offer.
Mata scored a brilliant free-kick in the UEFA Champions League win over Juventus for the Red Devils, levelling the scores up before United went on to snatch a 2-1 win.
Per Liam Twomey of ESPN FC, at times the former Chelsea man has been a bright spark for United in what has been an otherwise difficult campaign:
Herrera, meanwhile, faces a lot of competition for places in midfield, with Paul Pogba, Nemanja Matic, Fred and Fellaini also in contention for spots. However, the former Athletic Bilbao man is someone Mourinho regularly turns to in big games, as he's renowned for his tenacity and energy in midfield.
The 29-year-old has emerged as a leader for the Red Devils in recent years too and as noted by Paul Hayward of the Daily Telegraph, he isn't shy of sharing his opinions to the referee either:
The Spain international recently spoke about the unique demands that come with playing for United:
According to Luckhurst, the Red Devils are also looking to tie Ashley Young down to another year, with his deal also set to run out following the 2018-19 campaign.
While some eyebrows will be raised at the prospect of Young staying on, it'd make sense for United to keep both Herrera and Mata around.
Neither are players who represent shoo-ins in United's best XI, but in certain matches and certain situations they bring a lot to the table. Plus, if either player was available for free at the end of the campaign then there'd be plenty of suitors for the pair.