The England international has been linked with a host of different Premier League clubs in the summer transfer window.
Butland was linked with a potential switch to Liverpool FC before the Merseyside outfit signed Alisson Becker in a £67m deal from AS Roma.
Chelsea FC are facing uncertainty surrounding their number one goalkeeper Thibaut Courtois in the 2018 summer transfer window.
Courtois has been linked with a £31m move to Champions League holders Real Madrid to replace Keylor Navas.
Leicester City goalkeeper Kasper Schmeichel and Everton shot stopper Jordan Pickford have been linked with move to Chelsea FC.
Sky Sports News reporter Sheth suggested that Chelsea FC focus their efforts on the addition of Butland.
“The easiest one to get over the line is Butland,” Sheth told the Transfer Talk podcast.
“He knows he is number two at England. If he wants to be number one, he needs to be playing in the Premier League.”
Chelsea FC have won the Premier League title twice in the past four seasons under Antonio Conte and Jose Mourinho.
The Blues finished in fifth spot in the Premier League table last term to miss out on a Champions League spot.
MORE: Man United latest news
MORE: Arsenal latest news
MORE: Chelsea latest news
MORE: Liverpool latest news