A host of competitive offers has / have been received
Solution 1:
Technically has is correct, as the subject of the sentence is "host." However, if you think this construction will sound odd to your audience, it may be preferable to rewrite the sentence to avoid it. For instance,
Many competitive offers have been received.
or even
We have received many competitive offers.
which also changes the voice from passive to active.
Solution 2:
Plural. Use "have". "Host" here has no substantive meaning, but just indicates plurality (in an extreme degree).