The Toffees, who have lost all three of their Premier League matches this season, are in the market for a new striker, with Dominic Calvert-Lewin again on the sidelines.
Everton are being heavily linked with Udinese's Beto, but a proposed move for Southampton's Che Adams has allegedly broken down.
According to The Sun, the Merseyside club's head coach Sean Dyche is keen on a deal for Ings, who could be allowed to leave the London Stadium before the end of the window.
Ings previously played under Dyche at Burnley, and the pair are said to have a strong relationship.
The Englishman made the move from Aston Villa to West Ham in January, and he scored three times in 22 appearances for the club in the second half of last season.
Ings has featured twice this term, meanwhile, appearing off the bench against Bournemouth and Brighton & Hove Albion in the Premier League.
Meanwhile, according to journalist Yagiz Sabuncuoglu, Nottingham Forest are keen to explore the possibility of signing Michy Batshuayi before the transfer deadline.
The 29-year-old scored 20 times for Fenerbahce during the 2022-23 campaign, while he has already netted twice in six appearances for the Turkish giants this season.
Batshuayi's current deal is due to expire next summer, though, and there has recently been speculation surrounding his future in Turkey.
Forest are said to be showing a strong interest in the forward, while another unnamed Premier League club are allegedly keen on his signature over the next week.
The Belgium international has previously played in the Premier League for both Chelsea and Crystal Palace, netting 15 times in England's top flight during his professional career.
Forest are currently well-stocked in the final third of the field, but head coach Steve Cooper is said to be keen to add another proven goalscorer to aid the team's survival hopes.
Elsewhere, Philippe Coutinho has allegedly now come to an agreement with Al-Duhail over personal terms.
The Brazilian's future at Aston Villa continues to be called into question heading into the final week of the Premier League transfer window.
According to transfer expert Fabrizio Romano, Al-Duhail have now found an agreement with Coutinho over personal terms, with the experienced attacker offered a lucrative salary.
However, Romano claims that Villa are yet to give the green light, with the club said to be working on another attacking addition before allowing him to depart.
Coutinho has another three years left to run on his contract with Unai Emery's side, placing the club in a strong position when it comes to the negotiations.
The 31-year-old has found it difficult to make his mark for Villa since arriving at the club from Barcelona in January 2022, initially on loan, only managing six goals and three assists in 43 appearances.
Coutinho's best spell of his career came at Liverpool between 2013 and 2018, when he scored 54 times and registered 45 assists in 201 appearances for the English giants.