The 24-year-old spent the 2012-13 season on loan at St Andrew's and Redknapp has been keen to bring him back to the Midlands this summer.
The Italian side are said to have rejected Brum's approach, however, although Redknapp insists that he will not increase his offer as he believes Morrison is not "quite where he was".
"We made an offer, it was only a very small offer to Lazio because I feel Ravel is not quite where he was at, at the moment," Redknapp told Sky Sports News.
"He's been great, he's come in and trained well, worked hard, there's not been a minute's problem. But he's not shown me he's quite where he was.
"We've made an offer to keep him but it's not a big offer. We'll pay a part of his wages. If Lazio want to take the offer they can, if not he'll have to go back there."
Morrison, who spent the second half of last season on loan at Queens Park Rangers, has not featured for Lazio since April 2016.