West Ham launched a bid for the Cherries pair earlier this week, but it was immediately knocked back by Eddie Howe’s side.
Howe, himself, expressed his frustration at the bid - as it came just before Bournemouth’s final match of the season against Manchester United.
Bournemouth ended up losing the game 3-1, and Howe was frustrated that two of his players had to deal with speculation over their future prior to kick off.
The south coast side have already expressed a desire to keep hold of their key players, but they reportedly realise that there will come a time when the offers become too rich for them to refuse.
Bournemouth value Wilson and Ritchie at around £35 million, and the Mail suggest that they would accept offers of around that value.
West Ham have that sort of funds available this summer, but whether they will deem a move for the Bournemouth pair value for money remains to be seen.