One of the most striking things about the final decade of Ken Griffey Jr.'s career was that he never reached 100 RBI after 2000, even in 2005 and 2007 when he had over 30 HR.
From 1996-2000, he averaged 137 RBI per season, only falling below 134 in 2000 (when had only 118). Griffey finished his career with 1834 RBI, which puts him at 14th all-time (9 more and he would have shot past Ted Williams and Yaz to 12th place).
The all-time leader is Hank Aaron with 2297, which left Griffey 463 RBI short of the record. From 2001-09, he had only 559 RBI due mainly to injuries (62 RBI/season). Getting all the way to 2297 would have been a very heavy lift, even if he had been healthy (115 RBI/season from 2001-2009), but becoming one of he top 3 would have been easily reachable.
In order to become 3rd all-time in RBI, he would have needed an average of 90 RBI/season to reach 2080 and put him ahead of Cap Anson (kind of a surprise at #3, he managed 2075 RBI with only 97 HR from 1871-1897). There are still only 3 players with 2000 RBI: Hank Aaron, Babe Ruth and Cap Anson (Barry Bonds retired with 1996 RBI).
The next player to make a run at 2000 will probably be A-Rod, who has 1747 and is only 34. Considering that he is signed through 2017, he should make a run at Aaron's mark if he stays healthy.