The report claims the new Spurs manager is keen to add to his squad in January after landing an 18-month contract to take over from Andre Villas-Boas.
He will have some funds to strengthen next month, and is looking for a cut-price addition to his forward line. The report claims Gomis, a French international, would be available for as little as £5m after telling Lyon he wants to leave the club.
Summer signing Roberto Soldado has struggled to find the net from open play since his move from Valencia, although chances have been difficult to come by.
Jermain Defoe has been linked with MLS side Toronto, and the England international is expected to leave after failing to break into the first-team.
Emmanuel Adebayor has been brought in from the cold under Sherwood, and rewarded Spurs with two goals in a match-winning performance against Southampton last week.
But Sherwood wants options, and the report claims Spurs will speak to Lyon about his availability in the next few days.
The 28-year-old Gomis has been linked with Rubin Kazan and Newcastle in the past.