Maddon wouldn't tip his cap as to who out of the two is the favorite, but said they are who the team is currently looking at.
The Rays' skipper would prefer to keep Wade Davis, who started 29 games for the Rays in each of the past two years, in the bullpen.
"I want to talk to Wade Davis about it because I really like what he's doing in the bullpen right now. We will probably not go in that direction," Maddon said. "It's probably going to come from the Minor League area."
Archer and Cobb are not similar pitchers, according to Maddon, but they are both throwing well in the Minors and are ready to come up.
"Both have great arms," Maddon said. "Different pitchers in a sense. Archer [has] a little bit more dynamic arm, little bit more velocity. Cobb is a little bit like a Hellickson type; fastball, changeup kind of guy. Both good makeup. Cobb has done it before, did a great job for us last year. Both young with good makeup. We see both of them as being part of our future. They're both very interesting, they are both going to be very good Major League pitchers."
Cobb went 3-2 with a 3.42 ERA over nine starts with the Rays last season and is 1-4 with a 4.14 ERA at Triple-A Durham, but is coming off his best start of the season. He allowed no runs over five innings while matching his season high for strikeouts with eight.
Archer, meanwhile, is 3-4 with a 4.71 ERA at Durham and has won his last two starts. He is considered the Rays' No. 3 prospect, according to MLB.com