The Premier League new boys were reported to be in talks with the pair about a move to the south London club but Parish says that it is now unlikely to happen.
Quoted in the Daily Star, Parish said: "It's very unlikely Dan and Carlton will be signing, we have decided to move on.
"We are now looking at alternative targets."
Gosling has struggled with injury for most of his time at current club Newcastle United while Cole is a free agent after leaving West Ham and has also been linked with Hull City.
Palace start their league campaign with a London derby against Tottenham Hotspur.