The ex-Tottenham forward, who has now undergone a medical at Sunderland according to the BBC, was a transfer target for Palace but Pardew says the club were not quick enough to capture the 32-year-old.
Pardew went on to praise Sunderland's signing of Defoe and the 53-year-old admits the striker would have been a good solution for the Selhurst Park outfit.
Instead of the former Tottenham man, however, Palace this week confirmed the loan signing of Arsenal striker Yaya Sanogo.
"We tried to get Defoe but probably a bit late in the loop on that one," the Crystal Palace boss told reporters.
However, the Crystal Palace boss admits the Eagles were never that close to signing the 32-year-old: "I wouldn't say we were that close, no. It never really got to the stage where I got to speak to Jermain, so I would say we were not that close."
Sunderland have struggled for goals this season and boss Gus Poyet will hope the ex-Spurs striker provides the solution the Black Cats are looking for.
As for Crystal Palace, Pardew got off to a flying start as Eagles boss when he beat Tottenham last week. This weekend, Palace travel to Burnley, while Sunderland face Defoe's old side.