Former head of the British Army Lord Dannatt and former foreign secretary Sir Malcolm Rifkind had called for the move following the beheading of US journalist James Foley by IS militants.
"We may very well find that we are fighting, on some occasions, the same people that [Assad] is but that doesn't make us his ally," Hammond told BBC.
"It would not be practical, sensible or helpful to even think about going down that route," he added.
But Hammond argued that Rifkind and Lord Dannatt were both wrong.
"I do not think that engaging in a dialogue with the Assad regime would advance the cause that we are all advocating here," Hammond said.
He added: "General Dannatt I heard talking about the adage that my enemy's enemy is my friend. I have said very often that one of the first things you learn in the Middle East is that my enemy's enemy is not necessarily my friend.
"But that does not make us able to trust them, it does not make us able to work with them and it would poison what we are trying to achieve in separating moderate Sunni opinion from the poisonous ideology of Isil [Islamic State] if we were to align ourselves with President Assad."
Hammond, however, did not rule out Britain supporting the US in launching air strikes against IS and confirmed that the UK was looking "sympathetically" at calls to provide arms to Kurdish peshmerga fighters who are at war with the IS.
Meanwhile, British security forces are trying to identify the jihadist who had an English accent and appeared in footage of Foley's killing.
Unconfirmed reports suggest the man is from London or south-east England.
Hammond said authorities were "devoting significant amounts of resource to identifying the individual".
The government has defended its approach to extremists at home, following calls for a change in strategy prompted by the killing.
He said "significant powers" were available to deal with people planning to travel to Syria or Iraq to fight.
You’ve reached your limit of {{free_limit}} free articles this month.
Subscribe now for unlimited access.
Already subscribed? Log in
Subscribe to read the full story →
Smart Quarterly
₹900
3 Months
₹300/Month
Smart Essential
₹2,700
1 Year
₹225/Month
Super Saver
₹3,900
2 Years
₹162/Month
Renews automatically, cancel anytime
Here’s what’s included in our digital subscription plans
Exclusive premium stories online
Over 30 premium stories daily, handpicked by our editors


Complimentary Access to The New York Times
News, Games, Cooking, Audio, Wirecutter & The Athletic
Business Standard Epaper
Digital replica of our daily newspaper — with options to read, save, and share


Curated Newsletters
Insights on markets, finance, politics, tech, and more delivered to your inbox
Market Analysis & Investment Insights
In-depth market analysis & insights with access to The Smart Investor


Archives
Repository of articles and publications dating back to 1997
Ad-free Reading
Uninterrupted reading experience with no advertisements


Seamless Access Across All Devices
Access Business Standard across devices — mobile, tablet, or PC, via web or app
