The West Ham boss feels there is potential within his side to earn more international call-ups.
And Allardyce thinks right-back Jenkinson can also make an England team in the near future as the position is particularly problematic for Hodgson.
Speculation had suggested West Ham duo Aaron Cresswell and Mark Noble could make the English squad but it is Jenkinson's chances that the Hammers boss fancies.
“There seems to be a particular problem at right-back at the minute and I think he’s got the potential, based on my short time with him, of getting a chance," the 60-year-old told reporters.
“He’s been at Charlton, then Arsenal and he’s now playing regularly for us. It just seems that Kyle Walker has been out for a long time and Glen Johnson at Liverpool seems to get the odd injury here and there.
"Right-back has become a bit of a challenge for Roy - who are they? Where are they? And how good are they?”