Ba and Bertrand back for Blues' Wembley trip
Senegal international Ba, who was ineligible for Thursday's Europa League quarter-final at Rubin Kazan, suffered an ankle problem in last weekend's 2-1 Premier League victory over Sunderland and had to go off at half-time.
England full-back Bertrand, who has been deputising in the absence of the injured Ashley Cole, missed the trip to Russia due to illness.
Interim manager Rafael Benitez told a news conference that Ba and Bertrand took part in a light training session on Friday and he expected both players to be in his squad against City.
Cole and centre-back Gary Cahill are again out with long-term injury problems.
Second-placed City beat Chelsea 2-0 in the Premier League in February but Benitez said he learned some valuable lessons from that defeat at the Etihad Stadium.
"We know what we did wrong when we played against them," said the Spaniard. "We will try to do these things well on Sunday.
"City are in a good position in the table and they did well against Manchester United the other day," added Benitez, referring to their 2-1 win over the Premier League leaders on Monday.
"We know it will be difficult but it is a semi-final of a massive competition."
A much-changed Chelsea side lost 3-2 against Rubin in Moscow and squeezed through 5-4 on aggregate to set up a Europa League semi-final against Swiss club Basel.
The European champions have had five fixtures in 13 days and Benitez was full of praise for the way his players had dealt with their gruelling schedule.
"The squad are doing really well," he said. "They are working very hard and I can change players and still keep a good level so I am really pleased with that.
"It is an advantage [for City], I don't know how much but we are trying to manage our squad and team selection and we have some players with fresh legs."