Everton are still hoping to conclude a deal with Sevilla midfielder Steven N'Zonzi during the January transfer window as they look to wrap up a deal for Arsenal forward Theo Walcott before their clash against West Bromwich Albion on Saturday (20 January).
The Toffees are already overloaded in central midfield but Allardyce is a firm admirer of N'Zonzi, a player he signed as manager of Blackburn Rovers and even attempted to make eligible to play for England during his tenure as Three Lions boss.
Arsenal and West Ham United were also said to be interested in the 29-year-old, who made his intention to leave Andalusia clear after he fell out with former manager Eduardo Berizzo, who has since been replaced by Vincenzo Montella. N'Zonzi has a €40m release clause in his contract with Sevilla, who were apparently willing to accept a lower fee last month.
It is not known if N'Zonzi still has designs on leaving Sevilla, but Everton remain intent on signing the former Stoke City star before the end of the month, according to The Daily Mail, while Lille defender Adama Soumaoro is also an option they may look to pursue in the coming weeks.
Everton are in dire need of reinforcements for the left side of their defence due to concerns over the ageing Ashley Williams, Phil Jagielka and Leighton Baines, who has missed the best part of two months with a calf injury.
Soumaoro would provide a welcome tonic to the problem area due to his ability to play at centre-half and left-back, and he would also be available at a relatively low price of £18m, due to Lille's need to sell their stars in order to comply with Financial Fair Play requirements.
Swansea City defender Alfie Mawson has also been linked with a £25m move to Merseyside, but Carlos Carvalhal's side are reluctant to part with the former Barnsley centre-back as they battle relegation.
A left-back is of the utmost importance to Everton boss Allardyce, though he may not have to dip into the transfer market to solve that issue. The former West Ham United and Bolton Wanderers boss is keen to run the rule over Luke Garbutt, who was not registered in the Toffees' Premier League squad by former manager Ronald Koeman.
Garbutt has failed to deliver on the initial promise he showed four seasons ago when he impressively deputised for Baines, but Allardyce, who is hoping to shift some players out of Everton before the end of the month, is open to giving the 24-year-old a chance to revive his Goodison career during the business end of the campaign.