What chemicals could absorb/adsorb ambient atmospheric methane? From an article in the New Scientist in 2010, 


  Since pre-industrial times, methane levels in the atmosphere have risen from around 715 parts per billion to nearly 1800 ppb, claims Folberth. "If methane could be taken back to pre-industrial levels it would bring about half a degree of cooling and would be equivalent to removing one-third of anthropogenic carbon dioxide," says Folberth. Furthermore, the cooling would take place within 10 years.


Klaus Lackner and others have developed technology such as the moisture-swing sorbent to capture ambient $\ce{CO2}$

Where might be the chemical options for a material that would absorb or adsorb ambient methane?
There is none. Alkanes are very hard to activate. They require either free radicals, or coordinated unsaturated sites either in the molecule or on surface of solid. But in both cases, the atmosphere contains molecules that will react more readily.

However, the average life-time of methane in atmosphere is quite small, less than 10 years.