…undoubtedly the essay by J. Mark Beach in the Mid-America Journal of Theology entitled “Calvin’s Treatment of the Offer of the Gospel and Divine Grace“. It is a fair and balanced summary of Calvin’s teachings.
Here is Beach on the definition of “offer”:
The gospel is “the doctrine of salvation,” as such it “invites all to partake of salvation without difference….” Calvin then links the word invitare [invite] to offerre [offer]. “For Christ,” he writes, “is there offered, whose proper office is to save that which had been lost, and those who refuse [recusare] to be saved by Him shall find Him their Judge.” We should note that Calvin‟s language of “refusal” comports with the language of offer and invitation. It will not do to make these terms to mean Christ is “displayed” to sinners. Calvin‟s language is that a genuine invitation is given—a genuine offer and a genuine refusal.
Here is Beach on the “offer” as expressive of love:
Another place where Calvin speaks in clear gospel-offer language is Jeremiah 7:25-26. In his lectures on this text Calvin offers the following instruction: “We may hence learn a useful doctrine,—that God rises to invite us, and also to receive us, whenever his word is proclaimed among us, by which he testifies to us his paternal love.” Here Calvin defines the invitation as reception or at least demonstrates that the intention of invitation is reception; that is, the reason for God rising to invite sinners to himself is also to receive them. This invitation is nothing less than an expression of his “paternal love.”
Do read the whole article. It is very helpful.