CHICAGO (AP) _ Former Defense Secretary Donald Rumsfeld said Thursday that he would not seek the 1988 Republican presidential nomination because he cannot afford to finance a dark-horse campaign.

''I believe my qualifications are the best among any candidate,'' Rumsfeld said. ''But I am unwilling to incur a deficit without some way of paying it off.''

Rumsfeld, 53, a former Illinois congressman who has served in the Nixon, Ford and Reagan administrations in various posts, said federal election laws present a catch-22 situation.

''We could raise the money, but it would require that I do nothing else, or we could run with a deficit,'' he said. ''It's against the law to pay the deficit off yourself, or to raise funds to pay it off from anyone who has given previously.

''The election laws have arrived at a point where, although well- intentioned, they really create a barrier to entry.''