If the Toronto Blue Jays really want to hang onto Edwin Encarnacion, they're going to have to up their offer.

Encarnacion, a three-time All-Star who ranks among the greatest hitters in Blue Jays history, rejected a four-year deal worth about $80 million from Toronto before the club agreed to a three-year contract with Kendrys Morales, according to Jon Heyman of FanRag Sports.

Still, despite adding a full-time designated hitter in Morales, the Blue Jays remain interested in re-signing Encarnacion.

On Friday, Blue Jays general manager Ross Atkins suggested talks with Encarnacion weren't done, telling reporters that Morales' deal "by no means" eliminates the possibility of re-signing the 33-year-old, while conceding it's "slightly less likely." That said, there appears to be a considerable gulf between the Blue Jays and Encarnacion, who's said to be looking for a five-year, $125-million deal in free agency.

It remains to be seen if any club will pay that price, though. Encarnacion's agent, Paul Kinzer, said last week that things were still "pretty quiet," and two supposed suitors may be less interested than initially thought. Boston Red Sox president of baseball operations Dave Dombrowski recently said he's not looking for a full-time DH, while the Houston Astros may be less inclined to pursue Encarnacion, too, after acquiring Brian McCann from New York last week.

Related: Report: Red Sox, Encarnacion haven't had serious discussions

Encarnacion, who's attached to draft-pick compensation and turns 34 in January, is coming off another superb season in which he smashed 42 homers - tying his previous career high - while managing an .886 OPS (133 OPS+) over 160 games for the Blue Jays. Since 2012, only five qualified hitters boast a higher OPS than Encarnacion, who also ranks third in isolated power (.273) over that span.