Given their stature, many are expecting United to ease to victory against the League One side.
But Mourinho has warned his players about a potential slip-up against their opponents.
“We want to win, we know what cups are," he said.
"United played I think a couple of years ago at Yeovil and they know the difficulties they felt, so we have to go with a very strong team.
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“We are going to rest a couple of players, we have also a couple with little problems.
“We want to try to resolve to have them without problems for the next matches coming in February, Premier League and also Champions League, but apart from that we go with a very strong team.”
United last travelled to Yeovil three years ago.
And the Red Devils ran out winners on that occasion with Angel Di Maria and Ander Herrera finding the net.