Hodgson's defensive crisis deepened when Gary Cahill was forced to pull out of the squad through injury, following the withdrawals of Michael Dawson, Phil Jagielka and Rio Ferdinand.
Chris Smalling is in line to start at the Serravalle Stadium on Friday and could be partnered by Joleon Lescott but Hodgson is mindful of Tuesday's clash with group leaders Montenegro.
Lescott was booked in September's fixture against the Ukraine and another caution against San Marino would rule him out of what could prove a pivotal game in Podgorica.
Hodgson floated the idea of Carrick deputising in defence, as he has done for Manchester United on several occasions, before October's 5-0 win over Friday's opponents.
Newcastle's Steven Taylor has been drafted into the squad but is uncapped, while Tottenham's Steven Caulker has so far made just one senior appearance, in November's 4-2 friendly defeat to Sweden.
England can reclaim top spot in Group H if they win both matches.
Frank Lampard and James Milner both played down concerns over England's defence as they addressed the media on Tuesday, with Lampard saying: "These are the moments when you need a strong squad.
"It does happen in a funny way that you lose three or four players from the same position and that would test any squad, but we are very fortunate that we have got some very good young players and it will be time for them to stand up, and I am sure they can because they do it regularly."
Milner added: "We still have a strong squad, the players coming in are decent so I have no worries at all.
"Whenever Joleon plays he is ready to go, I see it every day at City. Steven Taylor deserves his chance too, he's been playing well and I know him from Newcastle."