Oliver Glasner is pushing the club to invest in a new forward in the upcoming January transfer window, with Johnson, 24, said to be their main target.
Aston Villa have also been linked with a move for the Tottenham winger, however, and Palace are now looking at potential alternatives.
According to the Daily Mail, Manchester City winger Bobb, 22, is on Palace’s list, although a loan move is looking more likely.
Bobb has struggled for regular first-team minutes at City, starting just five of his nine Premier League games, registering one assist.