The Toronto Blue Jays have not given up their pursuit of Chicago White Sox right-hander Gavin Floyd, major-league sources told FOXSports.com.

The Blue Jays are interested in upgrading their starting rotation before Opening Day. Toronto general manager Alex Anthopoulos made a very public scouting appearance at Joe Blanton’s start for the Philadelphia Phillies over the weekend.

The Blue Jays and White Sox have had dialogue about Floyd since the start of spring training, one source said. The teams have completed two trades since the end of last season, with relievers Sergio Santos and Jason Frasor going from Chicago to Toronto. The clubs also struck a three-way deal with the St. Louis Cardinals last July, in which Edwin Jackson went to St. Louis and Colby Rasmus to Toronto.

Floyd went 12-13 with a 4.37 ERA in 193 2/3 innings last year. His ERA has increased in each of the past three seasons. He is signed for $7 million this season, with a $9.5 million club option for 2013.

-- Ken Rosenthal and Jon Paul Morosi