Sage was appointed ahead of the season after Oliver Glasner departed to take charge of Nottingham Forest. However, his introduction to English football has proved difficult, with Crystal Palace struggling for results and sitting bottom of the Premier League table with seven points from their opening 10 matches.
Reports have suggested that Sage is expected to lose his position, with Palace keen to have a new manager in place before domestic football resumes following the international break.
Frank, who most recently managed Tottenham Hotspur after establishing his reputation at Brentford, has been strongly linked with the vacancy. His experience in English football and knowledge of the Premier League are understood to make him an attractive option.
Sky Sports also identifies the Dane as the frontrunner but reports that Palace are considering several alternatives rather than limiting their search to one candidate.
Former Chelsea manager Frank Lampard and ex-Burnley boss Sean Dyche are among those on the club's wider list. Vitor Pereira, Vitor Matos and Tony Popovic have also been mentioned as potential options.
One of the more interesting names is Hellberg, whose work at Middlesbrough has attracted attention.
The Swedish coach has impressed since taking charge of the Championship side, who are currently second in the table and firmly involved in the promotion race. His progress has brought him into consideration for a position at the highest level of English football.
Crystal Palace face an important decision as they attempt to arrest their disappointing start to the campaign. Their next appointment will need to provide an immediate improvement in results while restoring confidence within the squad.
Frank remains the leading contender, but Hellberg's inclusion demonstrates that Palace are also looking beyond established Premier League names as they assess the options available to them.