The world number four is said to have contacted the LTA about playing at the Aegon International at Eastbourne and they are reported to have offered him a wildcard - although nothing has been confirmed as yet.
Despite his recent indifferent form Djokovic, now coached by Andre Agassi, would be a major coup for the Eastbourne tournament.
The Serbian player has had a poor start to the year and his ranking dropped after failing to defend both his Australian Open and French Open crowns.
The 12-time Grand Slam champ and former world number-one had been considering a break from tennis after a comprehensive defeat to Dominic Thiem in the quarter-finals at the French Open.
He is still believed to be assessing his options ahead of Wimbledon and he is yet to finalise his preparations ahead of SW19 but Eastbourne is said to be a strong possibility.
The Lawn Tennis Association said that there is a possibility that Djokovic will participate at Eastbourne this year.
Djokovic has won Wimbledon six times and in the past has prepared by playing exhibition matches on grass a – a routine he has used for the previous six years.