Both players were missing for defeat at home to Everton on Saturday.
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McKenna said of Greaves: “He has an injury after the West Ham game, so he’s going to be out for a few weeks at least.
“And Ben Johnson got an injury very late in the training week this week, so we’re still assessing that one but it’s probably going to be a couple of weeks as well.”
Ipswich were beaten 2-0 at Portman Road by Everton yesterday.