Turner spoke after Wedbush Securities released a note to clients on Monday that suggested the online food-ordering company may be Amazon's next target after the $13.7 billion Whole Foods Market deal.
Wedbush argued that Grubhub would be a nice compliment to Whole Foods because the food ordering company has a similar geographic overlap and similar customer and diner demographics.
Turner also explained to CNBC that Amazon has two important food initiatives — fresh food and restaurants — and is likely not to let either "wither on the vine." Turner said in a note to clients that Amazon's restaurant delivery "was met with much sizzle, but lacked spice."
"Growth in both of those verticals is probably not as robust as they would have liked and they need to go out and make an acquisition to help support those initiatives," Turner, who has an "outperform" rating on Grubhub, said on "Squawk Alley."
CNBC has reached out to Amazon for comment.
Cowen senior internet analyst John Blackledge, also on "Squawk Alley," didn't say whether he thought Grubhub could be on Amazon's takeover list. He said, for the time being, Amazon will be focused on the Whole Foods deal.
They'll be dealing with "integrating it and really attacking what is the biggest retail market in the U.S., which is grocery," Blackledge said.
Blackledge also speculated that Amazon could make Whole Foods a multiplatform company alongside its Amazon Go platforms.