Millers boss Steve Evans has been in recruitment overdrive so far in the close season and has already brought in strike duo Kayode Odejayi and Daniel Nardiello.
Tubbs, who was prolific when playing under Evans at Crawley before joining the Cherries in January, attracted a "record-breaking" offer, while the offer for 20-goal Midson was also rebuffed.
"At a meeting with the chairman on Monday he sanctioned the offers for both Matt Tubbs and Jack Midson," Evans said. "In turn we have made two concrete offers but I can further confirm that both of them have been turned down.
"Both were good offers, in fact the Matt Tubbs offer was record breaking by some distance for Rotherham United.
"I have to say that both Tom Mitchell at AFC Bournemouth and Terry Brown at AFC Wimbledon spoke openly and I have taken their views back to my chairman so he alone can decide if he wants to put in any further offers."
