By SABC Sport
4th August 2024
Germany international Fullkrug, 31, was given permission by Dortmund to leave their training camp to discuss a £27million move to the Hammers, while Rodriguez is a free agent after leaving Real Betis at the end of last season.
Fullkrug and 30-year-old Rodriguez are undergoing medical tests on Sunday and Monday, before the deals are formally completed.
Fullkrug scored 16 goals in 46 appearances for Dortmund last season, helping them reach the Champions League final which they lost to Real Madrid.
Rodriguez was part of the Argentina squad who won the 2022 World Cup in Qatar.
The transfers continue a summer of rebuilding at West Ham after new boss Julen Lopetegui captured winger Crysencio Summerville for £25million from Leeds on Saturday evening.
Lopetegui has also brought in defender Max Kilman from his former club Wolves for ã40million, as well as goalkeeper Wes Foderingham and Brazilian winger Luis Guilherme.
Manchester United right-back Aaron Wan-Bissaka is understood to be another target for the Spaniard, although he went off injured during the Red Devils' 3-0 friendly defeat by Liverpool in South Carolina.