Standard Sport understands the Ukrainian is of interest to Tottenham, who have made it clear they are keen to take him on loan.
Spurs are also among the clubs considering buying Tosin Adarabioyo from Chelsea.
Mudryk has made it clear that his preference is to join a Premier League club on loan this summer.
Chelsea have made him available for loan but are not willing to loan him.
Spurs are interested but there are others, including Leeds. Chelsea rejected a loan offer from Leeds for Mudryk earlier this summer after feeling the terms were not desirable.
It is understood that Brentford also asked about the conditions of a loan deal over the past month.
Mudryk has also fielded loan interest from abroad, including from Italy, but continues to favour a Premier League loan.
To join Tottenham would see Mudryk reunited with Roberto De Zerbi. The pair worked together at Ukrainian side Shakhtar Donetsk before Mudryk moved to Chelsea.
Mudryk played under the Italian 19 times, scoring two goals and assisting nine in that time.
Tottenham and Chelsea are both expected to have a busy Deadline Day. Spurs have already spent heavily this summer but held talks with Everton to sign Illiman Ndiaye this week.
Mudryk may be one of several players to leave the club on Tuesday, with Dario Essugo expected to leave on loan and Robert Sanchez also tipped for an exit after the signing of Emiliano Martinez.