According to ESPN's Buster Olney, the Cincinnati Reds, Chicago White Sox and Texas Rangers are among the other teams in the mix. Sources expect Wheeler to net a deal in the neighborhood of at least five years and $100 million.
Wheeler's previous team, the New York Mets, are reportedly not believed to be in the running to re-sign him.
The 29-year-old Wheeler is coming off two strong seasons after struggling in 2017 on the heels of missing two seasons following Tommy John surgery.
After going 12-7 with a 3.31 ERA, 1.12 WHIP and 179 strikeouts in 182.1 innings in 2018, he went 11-8 with a 3.96 ERA, 1.26 WHIP and 195 strikeouts in 195.1 innings pitched last season. He set career highs in both strikeouts and innings pitched.
Gerrit Cole and Stephen Strasburg are the top two starting pitchers on the open market, but Wheeler is part of the next tier, and there may be some belief that he has untapped potential since he technically only has five years of MLB experience.
Few teams are in more desperate need of pitching than the Phillies. There were high hopes entering last season after they acquired Bryce Harper, J.T. Realmuto and Jean Segura, but they went just 81-81 and missed the playoffs for the eighth consecutive year, mainly because of their pitching.
Philadelphia's team ERA of 4.53 was 17th in MLB last season, and its 4.64 starters' ERA was also 17th. The Phillies do have an ace in Aaron Nola, but of the seven other pitchers who started at least 10 games for them last season, all had an ERA north of 4.00.
Wheeler would give the Phillies the No. 2 starter they desperately need, especially with Jake Arrieta on a club option for the 2021 season.
The Reds, White Sox and Rangers could all benefit from Wheeler as well, but they seem to be further away from contention than the Phillies. As for the Mets, they risk losing a talented starter who could blossom elsewhere if he leaves, but with two-time NL Cy Young winner Jacob deGrom, Noah Syndergaard and Marcus Stroman already in the fold, starting pitching is the least of their concerns.