The popularity of Yushchenko, who was swept to power in the 2004 Orange Revolution, is at an all-time low and he is expected to be defeated in the polls on January 17.
Viktor Yanukovich, Ukraine's opposition leader and likely Moscow's preferred candidate, is seen to have a lead over his long-time rival in opinion polls.
Yulia Tymoshenko, Ukraine's prime minister and a former Orange Revolution ally of Yushchenko, is currently running second, according to the polls.
Russia had been due to send a new envoy to Ukraine after the departure of its last ambassador, Viktor Chernomyrdin, a former Russian prime minister.
"Unfortunately, with the current [Ukrainian] administration there is practically no hope of a normalisation of ties with Russia"
But in a separate video blog published on his website, Medvedev said the strain between Ukraine and Russia "has hit unprecedented levels".
Medvedev also accused Yushchenko's administration of seeking to ship arms to Georgia, saying it "shares responsibility" with Georgia for the "crimes" committed in last year's war.
Ties between Russia and Ukraine have suffered in recent months following a pricing dispute over gas supplies, which caused large parts of Europe to be left without heating for two weeks in January.
Russia has also been angered by Ukraine hopes to join Nato, fearing the military alliance is encroaching on its sphere of influence.
Yanukovich, who draws his strength from the mainly Russian-speaking east of the country, has also criticised Yushenko over the country's relations with Russia.
"Unfortunately, with the current [Ukrainian] administration there is practically no hope of a normalisation of ties with Russia," he said, according to the Interfax Ukraine news agency.
"The first thing that we will do when we come to power is to create normal, neighbourly relations with our strategic partner Russia."