Manchester City would be interested in signing Raheem Sterling if he were to become available, according to Sky sources.
Tottenham have completed a deal for Cologne defender Kevin Wimmer and he will join them in June, Sky sources understand.
Shevchenko, the country's record goalscorer with 48 goals in 111 appearances, was last week handed the opportunity to succeed Oleg Blokhin in the role following Blokhin's decision to join Dynamo Kiev.
But the 36-year-old, who played for Dynamo, AC Milan and Chelsea in a glittering playing career, believes he is not yet ready.
"Representing the national team for many years was a great honour for me and with the team I enjoyed many memorable moments and vivid emotions," he said in a statement posted on the Ukraine Football Federation (FFU) website.
"I am grateful to the Federation for the high level of confidence they placed in me by offering me the chance to lead the national team.
"But I think today, to lead a team like Ukraine is a somewhat premature step for me.
"I hope the leadership of the FFU will react with understanding to my decision.
"I am confident the national team can get to the finals of the 2014 World Cup and, for my part, I am always ready to support our team to help get maximum results."
Ukraine are currently second from bottom in qualifying Group H. Although they registered a creditable 1-1 draw in England, they also lost at home to Montenegro and drew with Moldova.