To look at whether a club had bought (or tried to) a title you need to look at their net spend. If a club had only spent what they had sold players for it is unjustified to say they bought the title, if a club has spent well outside their income, it then becomes justified to say they've bought the title.
Since 2003 the clubs net transfer spends are
Chelsea £577,599,000
Man City £507,620,000
Man Utd £205,100,000
Liverpool £198,100,000
Aston villa £122,725,000
Spurs £98,550,000
Stoke £88,575,000
Sunderland £83,910,000
Hull £48,480,000
West ham £39,855,000
Norwich £39,515,000
Fulham £37,515,000
Southampton £33,765,000
West brom £28,306,000
Cardiff City £27,070,000
Swansea £22,770,000
Arsenal £17,305,000
Crystal palace £7,950,000
Newcastle -£4,800,000
Everton -£7,865,500
We can see which two teams it can be said have definitely tried to buy the title, Newcastle and Everton both in profit on the transfer market, it can be concluded villa have spent a lot of money to buy a higher league position than they've achieved. Southampton reportedly owe £27m in unpaid transfer fees.