The Government are considering their options after a wave of European politicians including EU Commission president Jose Manuel Barroso, EU justice commissioner Vivian Reding and Austrian foreign minister Michael Spindelegger said they will not go to Ukraine for the European Championships.
Tymoshenko is serving a seven-year jail sentence in a case Western countries have labelled politically motivated, and is on hunger strike after saying she has been beaten in prison.
England are playing all three group matches in Ukraine and Robertson had initially planned to go to at least one of the games but that may now change.
A DCMS spokesman said: "The Government is keeping the situation under review in consultation with EU partners."
Meanwhile, Amnesty International today claimed Euro 2012 is being jeopardised by a "criminal" police force in Ukraine where police "have tortured people in an attempt to extort money, extract a confession, or simply because of the victims' sexuality or ethnic origin".
Amnesty's European director John Dalhuisen said: "The Ukrainian government must take action now to stop widespread police criminality.
"Failure to do so will encourage them to continue acting as a law unto themselves and put Euro 2012 fans in danger from a force that is out of control."