Mr Rennie will tell Lib Dems that Nicola Sturgeon’s party has made a “sloppy assumption” people north of the border have “radically different” views on Europe than those in the south.
A recent Survation poll put the Remain vote in Scotland at 76% while UK-wide polling suggests a much closer race with the Leave side.
The SNP chose not to join the official campaign group to stay in the EU ahead of the June referendum, instead stating it would lead its own “positive campaign”.
The party has also said a vote to leave Europe could be a trigger for a second referendum on Scottish independence.
Mr Rennie will suggest the SNP’s criticism of the Britain Stronger in Europe campaign is unhelpful in the bid to prevent a Brexit vote next month.
He is expected to say: “Liberal Democrats across the UK are working hard to win a big vote for Remain. READ MORE: Nicola Sturgeon: Brexit will make Indyref 2 ‘highly likely’
“We are working in partnership with others in the Stronger In campaign even if we disagree on so many other political issues. We have been on the streets making the positive case.
“Meanwhile, the SNP has refused to join any other campaign yet have daily opinions about how the official In campaign is operating.
“When the SNP are not criticising the official campaign, they are postulating about the consequences of a Brexit for Scottish independence.
“The SNP should ditch the criticism and the self-interested commentary. Instead they should work with other pro-Europeans to win the case for Remain.
“The SNP seem to take for granted that Scotland will vote radically different from England and that a big Scottish remain vote is guaranteed.
“That sloppy assumption misunderstands the complex range of views that exists in Scotland about Europe. If the SNP continue to behave as they are, they could risk a growth in the leave vote.”