The City captain was stretchered off in our 2-0 win over St Polten on Thursday night following a heavy collision with Melanie Brunnthaler around the half-hour mark.
Our number five is one of several key players currently sidelined, with the Blues facing Everton on Sunday before taking on Barcelona ahead of the festive break.
Taylor confirmed that he spoke to Greenwood last night following the victory and will wait for the results before providing a further update on her recovery time.
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“The game finished really late and it was late before I made contact with Alex,” he said.
“She was okay, but of course we’re awaiting the scan obviously, which is taking place today and we’re just awaiting the results.
“We need to continue to assess. Hopefully she’s okay. She’s been crucial to us and what we’ve done, not just this season but seasons past.
“I thought the team adapted really well to that, Laia came into straight away and was good. Our thoughts are with Alex and hoping it’s a speedy one.”
However, the boss did have positive news to share on Naomi Layzell, Laura Coombs, Chloe Kelly and Jill Roord.
The latter two in particular have a strong chance of featuring against Everton on Sunday having recovered from a concussion and groin issue respectively.
Coombs and Layzell, meanwhile, trained with the squad again today as they both near a return.
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Asked about their likelihood of facing the Toffees, Taylor added:
“Yes definitely, especially Jill. There was an option to use her last night but we really didn’t want to.
“Effectively we didn’t have to in the end which is good for her and gives us a little more at the weekend with two games coming up.
“Chloe trained today and looked good. All being well comes through tomorrow unscathed and I think that’s an option for us on the weekend.
“Naomi and Laura Coombs both trained today. If they can get through tomorrow and tick off the bits they need to do they will help us with options for the weekend.
“In a sense, even missing Alex from last night, we probably look stronger on the weekend.”
Elsewhere, the boss provided further detail on Khadija ‘Bunny’ Shaw’s injury, which he confirmed as a lower leg issue.
The Jamaican pulled up the day before our win over St Polten, with the boss admitting she’s unlikely to feature before the new year.
Taylor did add that our top scorer for 2024/25 is seeing a specialist to help identify the problem.
He said: “No, it’s another one we’re still assessing. She’s seen a specialist this morning and we’re still waiting to hear back from them.
“It’s one of those similar to Alex and just awaiting more medical information and then we can hatch a plan and give you an idea of when that’s going to be.
“Bunny’s is not the knee. I think it’s the lower leg.
“It just needs a sense of more investigation, that’s all. It’s not the knee, it’s working down the lower end near the foot. That’s as far as I know.”