The 26-year-old winger has emerged as an unlikely target for the Red Devils who are being linked with a January pursuit.
However, Howe has no intentions of getting rid of one his key payers as the Cherries continue to adjust to life in the Premier League.
"Matty's (Ritchie) a good player so it's not a surprise to me he's linked to the top clubs," Howe told Sky Sports.
"Matt Ritchie on form and playing well is a threat to anybody.
"Whenever any of our players gets linked, it's not welcome by us. We're not a selling club and we certainly want to keep the squad together if we can in January and not the other way."
Howe added: "We'd have to see that (a United bid) on its individual merit, but certainly we're not looking to sell him."