WASHINGTON—President Trump is eyeing sanctions against Moscow this week as he grows frustrated by Russian President Vladimir Putin’s continued attacks on Ukraine and the slow pace of peace talks, according to people familiar with Trump’s thinking.

The restrictions likely wouldn’t include new banking sanctions, one of the people said, but other options are under discussion to pressure the Russian leader into concessions at the negotiating table, including a 30-day cease-fire supported by Ukraine that Russia has long rejected. Trump might also decide not to impose new sanctions.