The Goodison Park club managed a clean sheet in the win over Huddersfield on Saturday in Allardyce's first game in charge but they have struggled at the back this season, conceding 28 goals in 15 Premier League games so far.
As such, the new manager is understood to be keen to strengthen his defence in the New Year and Evans and Rahman have emerged as possible targets.
West Brom managed to resist interest from Manchester City in Evans over the summer and the former Manchester United man has also been linked with Arsenal in the past.
The centre-half is now a target for Everton, according to ESPN, but it remains to be seen as to whether or not Albion will be open to offers in January.
If Everton do decide to make a move the fact Evans is due to fall out of contract in the summer of 2019 could work in their favour, as if the Baggies can line up a replacement a deal may be possible.
Chelsea full-back Rahman has been sidelined for nearly a year with an anterior cruciate ligament injury but is close to a comeback.
The 23-year-old's chances are likely to be limited at Stamford Bridge and Chelsea are open to loan offers, although Everton could face competition with both Schalke and Monaco said to be keen.