The former Liverpool defender has overseen just three wins in 21 Championship games and the Mirror claim the Finn could be on his way out of the club as early as today - either by way of sacking or his resignation.
Sherwood is said to have been interviewed by Brighton before Hyypia was given the job over the summer.
The 45-year-old has been out of work since being relieved of his duties by Spurs but the Championship side could take a gamble on him.
As for former Liverpool man Hyypia, should he end up leaving Brighton, this would be his second unsuccessful venture into the world of management.
The Finn managed Bayer Leverkusen in the Bundesliga but was sacked earlier this year.
Should he face the same fate at Brighton, it could potentially free Hyypia up to offer his services as Liverpool's defensive coach - although that remains to be seen and would only be pure speculation at this point.
Hyypia's loss, though, would most certainly be former Tottenham boss Sherwood's gain, should the Mirror's report prove true.