Celtic claim a fee was agreed with Manchester City for John Guidetti prior to them taking the striker on loan.
Xabi Alonso claims no Premier League offers were put to him before leaving Real Madrid for Bayern Munich.
The 26-year-old, who is comfortable in the middle or on the left of a back four, could make his debut when the Cherries face Preston on Saturday, subject to Football League clearance.
Painter has made just three appearances for the Seagulls this year and manager Gus Poyet believes that is a result of Wayne Bridge's form.
Poyet told the club's official website: "Marcos is always a great professional to have around the club but he has not had a lot of chances to play this season because of the form and quality of Wayne Bridge.
"It's important for Marcos to be playing regular football so it was a good decision for him to move to Bournemouth on loan, where he can help them push for promotion out of League One.
"We hope that he has a successful remainder of the season."