Eagles boss Tony Pulis has stepped up his search for new faces after returning from a training camp in Austria and is hoping to pull off an ambitious double signing.
Sigurdsson struggled to hold down a regular starting role with Spurs last season and new manager Mauricio Pochettino appears willing to let him leave White Hart Lane.
The Iceland international, who joined from Swansea City in the summer of 2012, is thought to have a price tag of around £8m.
Campbell could not prevent Cardiff from suffering relegation in 2013/14, despite scoring nine goals, but is set for a swift return to the Premier League.
Reports suggest there is a £600,000 release clause for the 26-year-old, although Palace still have to agree wages with the former Manchester man and Sigurdsson.
Campbell's Cardiff team-mate Steven Caulker has also been linked with a move to Selhurst Park, but Queens Park Rangers and Southampton are believed to have joined the race for the centre-back's signature.