Both players have until December 7 to accept or decline the offer. Should they decline the offer and sign with another team, Oakland would receive compensation in the 2012 draft.
Willingham set new career-highs with 29 home runs and 98 RBI in 136 games last year for the A's, his first with the club. The RBI were the most by an Athletic since Frank Thomas had 114 in 2006.
He is a .262 career hitter with 132 home runs and 434 RBI in 799 games over eight seasons with Florida (2004-08), Washington (2009-10) and Oakland (2011).
DeJesus hit .240 with 10 home runs and 46 RBI in 131 games with the A's last year. The 31-year-old left-handed hitter was acquired from Kansas City for Vin Mazzaro and Justin Marks on November 10, 2010.
In 1,007 career games over nine seasons with Kansas City (2003-10) and Oakland (2011), DeJesus has hit .284 with 71 home runs and 436 RBI.