By George Bowden
BBC News
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.
Mr Johnson will phone Russian President Vladimir Putin in the coming days.
The prime minister, who will also visit Eastern Europe this week, said the UK would not tolerate Russian “destabilising activity, and we will always stand with our Nato allies”.
He added: “If President Putin chooses a path of bloodshed and destruction, it will be a tragedy for Europe. Ukraine must be free to choose its own future.
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.
The Foreign Office is expected announce tougher sanctions against Russia’s strategic and financial interests in Parliament on Monday.
Meanwhile, UK officials will be sent to Brussels to finalise the details of the latest UK offer as ministers discuss military options.
In addition to bolstering troop numbers, No 10 said this could involve sending defensive weapons to Estonia. Fast jets, warships and military specialists could also be sent to protect the UK’s Nato allies.
Nato’s 30 members include the US, UK, and Latvia, Lithuania, and Estonia – former Soviet republics that border Russia. Members agree to come to another’s aid in the event of an armed attack.
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.
The UK already has more than 100 troops providing training in Ukraine as part of Operation Orbital.
Orbital has trained 22,000 Ukrainian troops since 2015, and more military trainers were sent to the country earlier this month to support the training of Ukrainian forces to use 2000 missiles sent from the UK.
Mr Johnson has also asked defence and security chiefs to consider further defensive military options in Europe during a high-level intelligence briefing on the situation last week.
A second trip for the prime minister to meet Nato member counterparts is also being planned for early next month, No 10 said.