Cherries have a long-term desire to bring back Ritchie, who left for Toon in 2016, and midfielder Billing is a possible trade.
The Dane was left out of the squad in midweek and questioned social media reports he was injured.
His Instagram account wrote a now-deleted comment on a club fan page: "Didn't know I was injured."
Bournemouth boss Jason Tindall attempted to explain the situation after the midweek defeat to Derby.
He said: "I'm a little bit confused because Phil Billing didn't complete yesterday's training session.
"He came in. He went in to see the doctor, complaining of his hamstring. It's one I'll have to speak to Phil about himself.
"But in my book – if you're unable to complete the training session and you come in from that the day before a game - and you go and see the doctor complaining of your hamstring, it means you're not fit enough to be involved for the game."