Last season's top scorer Fryatt had his pre-season preparations hampered by a leg infection following surgery at the start of the summer.
Fryatt made his only friendly appearance against Real Valladolid last weekend, scoring the goal that gave the Foxes a 1-0 win over the Spanish club.
Oakley was forced off after an hour of that game after twisting his knee but the midfielder has trained this week with no ill-effects.
City boss Nigel Pearson has signed Sunderland striker Martyn Waghorn on loan until January 11.
New Swansea manager Paulo Sousa will take a near fully-fit squad to Leicester for his first game in charge of the Swans.
Full-back Angel Rangel has handed the Portuguese coach a boost by completely shaking off the heel injury that curtailed his season last time out, while Marcos Painter is back after missing the majority of the last campaign with a knee problem.
Long-term casualty Ferrie Bodde remains on the sidelines with a knee injury suffered in November but he is nearing a return, while Darren Pratley (shoulder) and Thomas Butler (hernia) are both missing following surgery.
Summer signing Jordi Lopez should play some part after improving his fitness while Stephen Dobbie will lead the line on what will be his competitive debut.
Sporting Life