Prime Minister Boris Johnson said the possible deployment would send a „clear message to the Kremlin“.
The defence and foreign secretaries are preparing to meet their counterparts in Moscow to encourage de-escalation.
Johnson will phone Russian President Vladimir Putin in the coming days.
The UK has more than 900 military personnel based in Estonia, more than 100 in Ukraine as part of a training mission, while a light cavalry squadron numbering about 150 is deployed to Poland.
Last month, Russia made three demands of Nato: Ukraine should be barred from joining; it should end military activity in eastern Europe; and should not deploy missiles in countries near or bordering Russia.
Russia has placed about 100,000 troops, tanks, artillery and missiles near Ukraine's border, but denies it plans to invade the former Soviet republic, which borders both Russia and the EU.
