The Scottish FA president Rod Petrie has written to his Ukrainian counterpart "to send a message of support, friendship and unity".
The SFA is in talks with Uefa and Fifa over matches with Ukraine following Russia's invasion of the country.
Scotland's men are scheduled to face Ukraine in a World Cup play-off semi-final on 24 March with the nations' women's teams set to meet on 8 April.
"Football is inconsequential amid conflict," said Petrie.
"But we have conveyed the strong sense of solidarity communicated to us by Scotland fans and citizens in recent days.
"[The SFA] have offered to support our Ukrainian colleagues' preparations as best we can in these unimaginably difficult circumstances."
Petrie also says his organisation "will not sanction the nomination of a team to participate in our scheduled Uefa Regions Cup fixture against Russia, due to be played in August" if the conflict continues. The Regions Cup is a tournament for European amateur teams.
"This will remain our position should any other fixtures arise at any level of international football," he added.
Steve Clarke's Scotland men's team were drawn at home to face Ukraine and the Women's World Cup qualifier is scheduled to take place in Kyiv.
Clarke is set to name his squad on 15 March, with the winner of the semi-final progressing to the play-off final on 29 March against either Wales or Austria.
The Scottish FA is also discussing the men's under-21 side's match in Kazakhstan on 29 March, given that travel there requires a flight through either Russian or Ukrainian airspace.