The Croatian striker is set to be the subject of a £7.5million bid from Leicester City in January and Davis hopes 'Gers can ward off the interest like they did in the summer so they can retain their leading scorer.
"I was delighted with the club's stance last time with Jelavic. I hope they do the same in the next window," he said.
"He's happy enough here and he's qualified for the Euros, too.
"He's scoring goals, you get to do that here, and that's good for his confidence. Hopefully the club can hold on to him in January because he's a big player for us.
"Ultimately nobody is bigger than the club but losing Jela - with Naisy (Steven Naismith) out as well - would be a massive, massive blow."