The proposed deal to sign Gutierrez, 30, will cost just £2.1 million, A Bola report. A deal is expected to go through in the coming days.
Gutierrez scored 19 goals in 36 games in all competitions last season for River, and also netted at the World Cup last summer.
Are Tottenham missing out?
Gutierrez is not thought to be high on Tottenham's list of priorities at present, but considering his cheap price tag, perhaps he should have been.
He may have just recently turned 30, but he would have added valuable experience to a forward line too dependent on Harry Kane.
The future of both Roberto Soldado and Emmanuel Adebayor remains unclear, but Gutierrez would have come in motivated to succeed, and could not surely do worse than either of the misfiring duo did last season.