The European Commission, the European Central bank and the International Monetary Fund drafted the broad lines of an agreement on Tuesday to put to Athens, according to Reuters. If agreed upon, it would conclude four months of acrimonious negotiations and release aid before the cash-strapped country runs out of cash.
While there is also scuttlebutt about whether Greece would exit the European Union, Kelleher, who is also the president of Morgan Stanley Institutional Services, noted that the Greek government does not have a mandate to take itself out of the EU. Instead, it has to be a referendum voted on by its citizens.
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Meanwhile, inflation in the euro zone was higher than expected in May, which Kelleher said was a nice surprise.
However, while it looks like QE is beginning to work in Europe, "it's very early yet and growth is still very subdued," he said. "I think we'll see this QE going on for some time."
In the U.S., he's concerned about liquidity in the fixed income market.
Morgan Stanley co-authored a report with global management consulting firm Oliver Wyman in March on the issue in March. According to the report, global banks have shrunk their balance sheets by about 20 percent since 2010, which has "significantly" reduced the liquidity in the secondary asset markets.
"We actually think that it's not just a question of rates going up and what will happen; it's also a function of whether there is an inherent systemic risk in the market because of regulations, which have actually cause dealers to reduce inventories, reduce repo balance sheets and not act as the shock observers they've been," Kelleher said.
"So it is probably my single biggest concern, this whole issue of market structure but it's very hard to quantify that."
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JPMorgan CEO Jamie Dimon and former U.S. Treasury Secretary Larry Summers have also both warned about the risks of reduced liquidity in the bond market.
—Reuters and CNBC's Matt Clinch contributed to this report.