The forward, who joined the Club over the summer, is yet to feature for the Cup double winners, having suffered an injury in training in August.
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The 30-year-old had been in red-hot form, helping the Lionesses to the semi-finals of the World Cup with six goals in as many games, earning White bronze in the Golden Boot awards.
Cushing explained the striker has taken a big step in her recovery with a return to training pitch action, while Georgia Stanway and Lauren Hemp are also progressing well.
Goalkeeper Karen Bardsley remains sidelined with a long-term injury.
“Ellen White has been running around the pitch today,” he explained. “She’s had her boots on and it’s really positive.
“From the games over the last seven days, there have been no issues (with fitness).
“Georgia Stanway is still out with a hamstring but we’ve had some really good progress with that.
“Lauren Hemp has been training non-contact over the last seven days.
“None of them will be available for selection tomorrow but we’ll leave it with the medical team.
“The group we have available will be ready for the game.”
City v Lugano will be shown live on Man City for TV. Kick off is at 7pm.
City return to Champions League action on Wednesday night with the visit of Swiss outfit Lugano.
Cushing’s side stormed to a 7-1 away win in the first leg but the manager expects his squad to maintain their standards in a bid to build momentum and extend our impeccable opening to the campaign.
“I don’t really have any techniques as such (to maintain mentality at 7-1 up),” he added.
“It’s about the understanding that this performance plays a huge role in the weekend’s game against Everton – irrelevant of the score, we want to put in a good performance and play like we have been.
“Otherwise, we would go into the game almost on a negative. It’s irrelevant whether we go through with a win or on aggregate – the performance has to be there.
“Everton are up there with us – they’ve started well and they look really improved.”
City lifted both domestic cups last season, clinching the FA Cup for the second time and Continental Cup for the third.
Cushing’s side also won the league in 2016 and have reached the semi-finals of the Champions League in our first two seasons.
Asked whether the elusive European trophy sits as his main priority this term, Cushing replied: “I wouldn’t say it’s a priority.
“The league is always the priority – to be the best team domestically and dominant has always been at the forefront of our mind.
“The Champions League is there. We got to two semi-finals in three seasons and we weren’t able to make it into the Final, although we did show progression.
“It was a huge disappointment last season so that’s a motivation in the background to go as far as we can.
“We understand how difficult the competition is.”
